I've started getting this message when I try to save. It tells me to delete saves (obnoxiously, I have to "Agree" before I can do anything else), but it won't let me delete anything. Even worse, it looks like the last save it actually saved was from about 30 turns ago! Anyone have any ideas?

so lets cover the basics as you clearly don't play ironman mode [only one save]

are you using a Galaxy install or the off line?
have you got \signed into a Paradox account whilst playing?

the default location for Stellaris is your Documents\Paradox Interactive\Stellaris\save games... if you played ironman mode then it would be Documents\Paradox Interactive\Stellaris\pops_filestorage\save games

are these folders inside a dropbox, onedrive or some other network controlled space?

if your saves are in a onedrive then this will be a permissions issue i.e, onedrive only allows X and you have fills the box