Is there a post-game?

[Visuwyg]

I am just before the last Ford Fragment and a message popped up saying something along the lines of "this is endgame, finish up everything else before you proceed".

Should I finish up all sidequests and try buying all pins now? Or can I finish the story and clean up afterwards. (I am still missing a psy power I believe, as there is a spot left on Raz' bag. And there are these mailslot doors I can't access)

[( ͡° ͜ʖ ͡ °)]

You can keep playing after finishing the story.

[AlisterCat]

Once you move in to the next part you won't be able to go back to do all that stuff for a while, but once the game is finished you will have access to all of it again.

[Clockwork]

some things cant be collected until you have beaten the game

[Gorlom[Swe]]

Progressing further locks you out of the old overworld/real areas, but you have access to the otto-matic and braintumbler in the new area so you can still visit old brains and you can still buy pins in the new area. And as Clockwork says you can't collect somethings (such as the items through the mailslots you spoke of) untill after the credits roll.