It's not much really. Just like the first few episodes of the previous seasons, these episodes are setting up the scene for the rest of the season. Giving a solid ground to build upon.
So now we know that Eclipsa took over and treats monsters fairly. She doesn't seem to care all that much about the mewmans though. The remains of the Mewni Kingdom are in tatters, the people are distrustful and hopeless.
But the monsters are thriving. Baby Meteora didn't really stop from being a threat, seeing how she remembers Marco. The Butterfly family isn't as royal as some were led to believe but we knew this already from the newest merch book. Star is powerful enough now to not need a wand.
Star and Marco's relationship seem positive and not as awkward as it was before Booth Buddies. At least they got that shit out of their system. Maybe. Also the beach day photo is going to happen in the future, probably the near future (as in midseason).
Tom seems to have some difficulties with Star, he can be a bad demon boy all day long, but doesn't seem to have the logical or empathetic mindset Marco has. This was also shown in the episode where the monsters leave the mewman dimension, where he tries to come up with something nice to say, but he can't, because even though he IS a monster (are demons monsters or are they a separate category?), he is also royalty, and probably filthy rich. He can't really relate or comfort monsters who were mistreated.
Finally, Moon has been almost completely mindwashed from being exposed to the magic dimension for too long. But at least she still remembers how to bake pies. Oh and that one song from her and Star's childhood. The Butterfly family... is homeless. Probably. What with the mewman castle being torn apart. But it seems like Eclipsa is welcoming of them, seeing how she lets Star and Marco have their own room. Not sure what opinion Globgor will have on mewmans...
That leaves Ludo, the MHC and Earth up in the air.