This is a first draft of the dynastic politics that led to the PIC in the seventeenth century.
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The eldest son Ivan succeeded to his parents' realms piecemeal. Basil arranged for the Sejm to elect him king of Poland when he was still very young. Almost immediately thereafter Kristina abdicated her throne to him. He ruled both countries until his father's death in 1679, when he was crowned Tsar, uniting the three crowns for the first time. Ivan was a warlike ruler, attacking Turkey and expanding his borders to the east. He also took steps to make the unification more permanent. He established the first joint institutions in the Baltic and used the Swedish navy to seize control of the Duchy of Courland's small Atlantic colonies. He expanded the city of Nyen, laying the foundations for the great imperial capital at the head of the Baltic. (... I've referred, sort of ridiculously, to "St. Petersburg" in previous posts. With no Peter the Great, obviously the city is not going to be called that. Nyen is the older Swedish name for it, and it works just fine.) Domestically, Ivan, or Jan, was most concerned with shoring up his support among the Polish nobles. He married a daughter of the powerful Sapieha family. When Ivan died after more than twenty successful years, he was able to pass all three crowns to their son Kasimir.
St. Petersburg was named after Saint Peter the Apostle, via the original Peter and Paul Citadel along the Neva river. Peter the Great was, obviously never considered a Saint, so he is not officially the city's namesake, though he probably felt drawn to St. Peter at least partly due to the shared name. Another name you might consider is "Pavelgrad," after St. Paul. A third might be Derzhevnaya, a word meaning "Sovereign" which refers to the Virgin Mary in Russian iconography. A name based on that would have multiple layers of meaning, but I'm not well-versed enough in Russian to make a grammatically correct placename.
That's not to discount relatively widespread multilingualism. Most educated people in the ASB can speak and read two of the main languages. The linguistic situation can probably be compared to Central and Eastern Europe, especially before some of the ethnic cleansings of the 20th century. You grow up exposed to several languages both in school and in your community. This is truer in some places than others. The central parts of New England, the Virginias, and Canada are notorious hives of monolinguals. Most of the island states, too. These people would definitely need travel handbooks to help them find services, along with that old staple for travelers, the phrasebook. "I will not buy this record, it is scratched."
This makes me want to create a Boreoamerican equivalent of
L.L. Zamenhof... what would an American Esperanto look like?
You're right, I wonder if this world would see anything like American car and road-trip culture. Something about it smacks of an echo of the pioneer ethos to me. A generation after the "End of the Frontier" in 1890, restless Americans were starting to use their cars to capture some of that same adventure. I haven't read specifically about that, so I may be wrong, but that's how it seems to me. If I'm at all right, that whole culture is certainly going to be very different in a world where that ethos didn't exist or was channeled in other directions.
In a lot of ways, traveling between the states must have felt a lot like international travel until quite recently. I know that road-building is a state responsibility and most highways are managed by states or consortiums of states. Only a few special highway projects are managed at the confedederal level. No doubt it was a common thing to be going down a decent highway only to get completely stuck in mud when you cross into a state with a smaller transportation budget. Railroads, usually built as they are by private companies that cross state lines, probably needed more confederal supervision.
It's an interesting hypothesis, and I've not considered that possibility, though I think the causes were more varied than that.
Wikipedia links the Grand Tour to road trip culture, although I'm a bit skeptical of that. The Grand Tour was for the wealthy youths to travel to the most cultured cities and get smashed in them while ostensibly getting educated, while American road trip culture was more about the freedom to go anywhere you wanted, whether small towns or large ones, and getting smashed in them while ostensibly finding yourself spiritually.
From 1900 to 1930, oil companies developed increasingly complex and increasingly efficient methods of delivering fuel to increasingly numerous cars, which brings up a major difficulty in creating auto culture in the ASB: The territory covered by the ASB IOTL had already depleted its oil supplies by 1910. The oil fields in Pennsylvania, Ohio, Indiana, and Illinois peaked between 1900 and 1908, and the oil fields in Oklahoma and Texas belong to Mexico ITTL. It would not be until the 1940s when offshore drilling became profitable, meaning there may simply not be enough oil to support automobiles for the majority of households as there were IOTL by 1930. The ASB would instead have to pay for Mexican oil. Or, maybe, Oil companies in the ASB would partner with the Mexican government to extract oil from OTL Oklahoma in exchange for tariff-free exports to the ASB. It would work for a little while, until the Mexican government decides they deserve a bigger slice of the pie, at least. Here's an idea: Bormex, short for Boreoamerican-Mexican Oil Company, being one of the major oil producers in the modern day.
In the 1910s, with more cars becoming available, long-distance trails, marked and maintained by auto organizations, came into being. These would form the backbone of what would become the US highway system in 1926. The most famous highway, Route 66 ran from Chicago to Los Angeles; in 1932, the Los Angeles Summer Olympics happened, attracting tourists, and the increasing agriculture in California attracted migrants from the Dust Bowl states. Route 66 became a major road. As Los Angeles grew more and more in tandem with the highway, the famous highway became more than a road, but an icon.
Once the cars and the oil were available to the average consumer, the enforced conformity of the early 1950s became a breeding ground for youth resentment. I think this conformity mostly stemmed from the US's involvement in WWII, as it saw the entire country pulling together in the face of a common enemy, typically silencing dissenting voices in the process. In addition, the parents of the disaffected youths were typically GIs who were taught conformity as part of military culture.
In this environment, Jack Kerouac (Who was a French-speaking Massachusetts man of Breton extraction via Canada- would be very at home in the ASB) wrote
On the Road, a mostly autobiographical novel based on his own journeys across the United States during the late 1940s that featured lots of sex, drugs, and spirituality. When it was published in 1957, it resonated with a lot of young people who felt constrained in this conformist society. In 1962, John Steinbeck wrote his own road trip travelogue,
Travels with Charley, in which he wrote about America and the varied people within. These two books cemented the road trip as the quintessential American journey, where one could exercise their personal freedom, discover themselves, and discover their country.
With the cosmopolitan nature of the ASB, I think that last point would probably resonate most strongly with its citizens. I'm imagining a counterculture movement of the 1960s- not a single movement but a loose collection of movements, where disaffected youths from one part of the ASB choose to move to other parts of the ASB because they feel it's closer to their ideal. This leads to weird random artist colonies in mid-sized cities where you don't expect them.
