I mean it can be both (broadly speaking). NATO loves expanding and broadening the strength of its alliance, weakening a geopolitical enemy, opening up new markets for their shiny shiny weapons, and provoking a little low-level conflict to keep everyone alert and stay on top of new tactical developments now that the landscape of war is changing.
But also, holding Russia at bay is a necessary noble thing to do, and all these breakaway republics are acting out of pure self preservation necessity when they join an alliance that will bloody Russia's nose for them if they get messed with.
All Russia had to do was join NATO and stop claiming the former Soviet Union has to be restored. NATO exists because Russia was considered a threat. Were it not a threat, its entire existence would be futile.
NATO was on the decline in the last decade. There were many articles asking if it was just a cold war holdover and many countries weren't paying their fair share. Then Russia invaded Ukraine, starting the largest war in Europe since WWII, and suddenly new countries are joining NATO and members are increasingly paying their 2%.
I find the term "Breakaway Republic" rather problematic. Most of the countries that used to be in the Warsaw Pact or USSR were independent before World War II. They did not just break away, they re-established their independence.