Don't do it publicly (on LinkedIn).

Instead, do outreach. Think of former co-workers you'd like to work with again. Or think of 10 companies you'd like to work at, and see if you know anyone there.

Reach out to these folks and say you're looking to explore your options, but want to be discreet. Have coffee. Ask questions about the problems they are working on. Send them a copy of your resume if you think it'd be a fun move and they agree it makes sense. (Make sure you update your resume for this purpose.)