How to bring back the proposition for war in Stelaris

No, an alliance goes to war entirely or not at all. You could demand vassalization from a one-planet empire though.

You occupy the planet, you do not control it, this works similar to EU4.

The occupation grants a large amount of warscore and you can send your armies away, Your opponent has to reinvade to liberate the planet.

Whether you get the planet in the end depends on the war goals, the occupation merely provides additional warscore, with which you can press your demands.

Most importantly though, it prevents the enemy from using the planet and getting resources from it without you having to constantly bombard it and requiring an invasion from your opponent to liberate it.