Well, apart from Francisco Franco finally getting into the Spanish Navy (even if it's in San Juan, not Havana) and Pablo Casals probably not inaugurating the festival as a result of being a Civil War refugee (not to mention no J-Lo and Marc Anthony), . . .
The effects on Puerto Rico would be huge if it remained Spanish. At the time of the Spanish-American War, Puerto Rico's cash crop dependent economy had reoriented itself around coffee and tobacco (sugar was but one component, and even then it wasn't a major driver of the economy as it became under the US) so those two crops, along with tropical fruits, remain the main drivers of Puerto Rico's economic development. Meanwhile, after the loss of Cuba and the Philippines, you'd bet Madrid would want to pump huge amounts of investment into Puerto Rico as its last remaining element of the Spanish Empire in the Americas. In that case, Puerto Rico would not be immune from broader Latin American trends towards Comtean positivism, although in this case it would like the US's contentious relationship with Central American and Caribbean countries rather than the paradigmatic examples of Mexico and Brazil. So alongside agriculture, the service sector (i.e. construction, the military) would also be a main part of the Puerto Rican economy - even more so as the Spanish are trying to replace what they already lost in Cuba in terms of infrastructure and all that jazz. Politically, while an autonomous province of Spain, the Puerto Rican political climate would differ considerably from the Mainland, even with superficial similarities, and would share strong similarities with other similar Latin American countries during this time period since Comtean positivism was A Big Thing (TM) that Latin American political élites thought could help their countries in particular and the wider region in general "civilize" and achieve modernity without changing the basic structures inherited from the colonial period. In fact, I'd go further - alongside this positivist consensus, similar to Colombia Puerto Rico would also retain its historic conservative and liberal parties, since they too accepted this consensus, with the Liberal Fusionists' Puerto Rican branch even branching out into populist-esque liberalism similar to its contemporary in José Batlle y Ordóñez and his Colorado Party in Uruguay.
Similar to
@Drex in assuming an OTL path for Mainland Spain (probably not), then the post-WW1 crisis would hit Puerto Rico very hard, leading to dissatisfaction with the positivist model and looking for options for change; Primo de Rivera's dictatorship would be more of the same of reheating a past-due positivist model on the Island. One option would be corporatism, and in this case I'd assume that a split would develop in Puerto Rico's conservatives which would allow it to happen and probably along the lines of Italy's People's Party (IOTL a similar split occured in Chile with its nucleus in the Falange Nacional; despite the name, it was actually made up of progressives and reformists and would form the basis upon which Chile's Christian Democratic Party would be built), so while it would start off as a big-tent corporatist party which would generally be conservative and focused largely on defending Catholic interests (as were the first generation of Latin American Christian Democratic parties in those days, cf. Mexico's PAN) it would be the reformists who would drive the agenda of the Catholic-corporatist party. Another avenue for change would be towards the Left, and in a more unusual way (well, more unusual by Spanish standards, but was emergent and was among many options on the table in Latin America and which ultimately had major impact in the region). Socialism and Marxism never really took hold in its canonical form in Latin America, with the few successful examples serving as exceptions which prove the rule, primarily because the ideologies developed in an environment assuming a stage of political, economic, and social development that approximated Western Europe and North America as the paradigm that it wanted to change, not to mention that Marx himself believed his form of socialism could never work in Latin America and used all sorts of racist justifications to explain why. So socialism was largely a phenomenon limited to the immigrant populations until you had people trying to adapt both to fit into a Latin American context. The most successful of these (although not in its native Peru) was Victor Raúl Haya de la Torre and his American Popular Revolutionary Alliance (APRA), and it is parties in the same mold as APRA throughout Latin America that were among the most successful parties of Latin America's Left post-WWII since they were able, in their own peculiar country-specific environments and with a great deal of moderation so that they could be considered equivalent to social-democratic parties in Europe, to put Aprista policies into practice. Puerto Rico has one such Aprista party IOTL, the pro-status quo Popular Democratic Party (PPD) with its implementation largely manifested in Operación Manos a la Obra (Operation Bootstrap) and the creation of the modern Commonwealth as we know it today, among both non-Puerto Ricans (like yours truly) and Puerto Ricans alike; any attempt to replicate a party in APRA's mold in a Puerto Rico still part of Spain ITTL would need to take into account the social structures of Puerto Rico itself and the nationalist movement. There has always been discontent in some form or another on the Island (the most famous example being the Grito de Lares) and as some have already pointed out in this thread there's also been considerable racism in Puerto Rico historically, which dates back to the colonial-era class system which in a weaker form would still be prevalent. So something like Aprismo would hold special appeal for Puerto Rico's poor and lower classes, not only as a chance to better oneself but also as an acknowledgement of the realities of mestizaje on the Island itself as a core part of its identity and also by channeling the discontent in the Island into something more positive and constructive. (Conversely, parties like the PSOE, the Communists, and even left-liberal parties like Azaña's crew, for example, would hold little appeal in Puerto Rico since it would assume a situation similar to the Mainland that simply does not exist in Puerto Rico; Puerto Rico's Aprista party and the PSOE would not get along from the outset.) Now, this Aprismo could be channeled through the nationalist movement (which would ultimately advocate for Puerto Rican independence), through other means, or through both, with both a moderate-nationalist form of Aprismo similar to what IOTL would become the basis for the PPD and a radical-nationalist form of Aprismo that would advocate for independence. Either way, the Second Republic and Puerto Rico would not get along well since the Island would go for local parties which by Spanish standards would be centrist to right-wing but which by Latin American standards would be all over the spectrum. At its core would be problems resulting from the huge dependence on agriculture in the Puerto Rican economy which would mean the 1920s would be anything but golden/"roaring" in Puerto Rico and the 1930s would have the Island suffer the full effects of the Depression.
Therefore, when we reach the Civil War period (which already has one butterfly in Franco as a naval officer, possibly in Puerto Rico itself, which throws all sorts of Spanish military and colonial history into a different direction), my best guess would be that Puerto Ricans in general would be in an ambiguous position, preferring not to support either side and would much rather go its own way into neutrality. I don't think there would be strong feelings towards either side of the conflict since to do so would put the Island into a paradox. If Puerto Rico declared for one side or another, the problem that results is that the Island's population would refuse to go along and would lead to all sorts of contortions, i.e. Apristas supporting the Nationalists if the Puerto Rican government declared for the Republic, or Catholic-corporatists and hardline conservatives supporting the Republic and the Spanish Navy if the Puerto Rican government sided with the Nationalists. It would also make it all the more likely that the radical nationalists (the ones who, in IOTL as part of a much broader movement, sided with the Partido Nacionalista and its leader, Pedro Albizú Campos) would take advantage of chaos on the Mainland to declare an independent Puerto Rico and would be willing to fight both sides in order to achieve this objective - and the
last thing both sides want (particularly the Republicans, considering the chaos already present in its territory, not to mention the anarchists in Catalonia and Aragón) would be yet another piece of Spanish territory breaking away to form its own independent nation. So it would sue for neutrality and would hope and pray that nobody on the Mainland takes notice. This could mean that at the end of it Puerto Rico could go either way due to its neutrality, either as the last remaining bit of the Republic in a Taiwan-like situation, as another victory for the Nationalists towards the end of the Civil War out of indifference, or even as an independent state (and in this case probably backed not only by the US but also by the Dominican Republic under Rafael Trujillo, by Britain (the BVI are not far from Vieques and Culebra) and by other Latin American countries). No matter what form it takes, I do think a lot of Civil War refugees would try to make the crossing and their presence could definitely help Puerto Rico's post-WWII recovery. If Puerto Rico remains Spanish - either as a Taiwan-like remnant of the Republic or as part of Nationalist territory - I agree that decolonization would not be forced by the UN,
but that does not mean that the sentiments behind it will not go away, particularly among the Apristas and the nationalist movement. Furthermore, if Puerto Rico ends up either as an independent state or as a Taiwan-like remnant of the Republic, it's going to be subject to a lot of American economic and cultural influence - not as intense as IOTL, and definitely not to the levels of, say, Cuba, but the United States would become a major player in the Puerto Rican story. If the Republic wins the Civil War, OTOH, then we'd be entering into new territory and the Republic would have to hope the Nazis don't invade because then things will get bloody fast. Of course, if the Republic survives a Nazi invasion, then it would be a good time for the Republic to eschew its radical beginnings and moderate into something more acceptable to Puerto Ricans - or at least something that would make Apristas comfortable.