Is it right to mention Glassdoor, Blind, levels.fyi, etc when negotiating an offer?
You definitely can
"Can I wear my pants backwards?" - "you definitely can." Doesn't mean that you should.
Sometimes the recruiter says: what are your expectations? Mine are based on levels.fyi, so why not mention it?
Because you don't want to be known as the person who makes important decisions based on hearsay. Don't tell the recruiter that your expectation is based on levels.fyi.
No
What do you suggest then? Should I just say what I expect?
Competing offers and your current compensation is your only real leverage.