EDIT: Scrap that. After a while it starts running at 100% CPU on my macbook. I'm editing a small, simple PHP remotely over SSH. I haven't yet tested if it only happens with remote editing. Too bad... Well, at least it didn't trash the server like VSCode.
EDIT: Logs showed it was trying to do some auto suggestions every few seconds, but failed due to missing credentials. Didn't seem like something that would eat up 100%, but after disabling all AI features (I'm glad there was an option for this), the problem disappeared, and I'm happy with Zed again.