Also Santa Cruz is in his 70s now. He is coming up on his OTL death date. And even if lives longer his focus may be on leaving a house well in order for his successor.
Say what is the plan regarding succession? Is power going to devolve or has he groomed a second Supreme Protector? Either way I expect the Supreme Protectors' health is a major concern for people of the Confederation.
So Santa Cruz may not be in the big risk kind of mood right now and prefer to play it safe in foreign affairs to focus on his legacy at home.
Hmm, though if his before the war ends and there is a successor, they may approach the Alliance to enter at the endgame to solidify their rule with a victory and a few bits of territory.
Right now Santa Cruz is debating on what exactly to do for succession of the Confederation. The structure of the Confederation is that the nation is divided into three autonomous states; the Republics of North Peru, South Peru, and Bolivia. Each Republic has its own legislatures which deals with laws of their respective state, along with a regional president which is head of the regional assembly and has the rank and powers of an equivalent U.S state governor. As Supreme Protector, Santa Cruz is the national government and rules as dictator on a grand scale. The only national institutions are the Army, Courts, Foreign Affairs Office, Economics Ministry, and Postal service. Right now Santa Cruz does have a Supreme Protector who he has groomed to succeed him, but he is also debating on establishing some liberal reforms which will lead to a Confederate Congress, along with possible elections for the Supreme Protector. No matter what the office of Supreme Protector will have the largest amount of power in the Confederation.
I am not sure they would get anything if they did not do any fighting. Argentina is not a fan of Santa Cruz as he beat them in the last war along with Chile.
Also this war I think will still be very nasty. As Kaiser said on the matter of Napoleon III the way history has played out has made him be seen and be remembered as a great ruler and get credited it seems for ending the political turmoil that dominated French politics for nearly sixty years.
Likewise, I have read some stuff on Paraguay that foes give some kudos to Francia and Lopez the Elder, such as building a more racially integrated society and infrastructure. While the IU history sees them as nothing but irredeemable despots. So I am thinking Paraguay's fall to both the inside and outside will be so bloody and arduous that it would not cross most people's mind to associate anything good with Paraguay much less its leaders.
And after such a bitter struggle I don't think the Alliance would be willing to give even meager prizes to a noncombatant nation.
But back to Santa Cruz, his exit will be huge. He founded the Confederation and has been its autocrat for more than two decades. The Supreme protector and the Confederation I would say are synonymous with many within and without its borders. When he is gone there will not only be shifts inside with either his heir or a new government, but outside with the PBC's enemies and rivals adapting their policy.
OTL's war was already bloody with 90% of the entire male population of Paraguay being killed in the war. Expect something along similar lines.
The reason Paraguay is seen as nothing but a despotic kingdom is partly due to narrative reasons. You see the author (TTL version of me) is kind of a biased man when going into the vast history of his world, and as such he may view certain events in a perspective depending on their impact and the immediate legacy surrounding them. While historians TTL can recognize the non-racial society that was made by Francia and Lopez, they cannot view the full legacy of that since Paraguay will fall in a few years, meaning there isn't much results to back it up. Had Paraguay survived then maybe these rulers would be looked at in a better light. But because Solano's Lopez actions led to the downfall of his nation, people are more willing to look at the bad rather than any of the good.