Fired from boutique hired by BB, Old MD and new MD know each other, update LinkedIn or wait till probation ?

Was performance managed out of role and have joined competitor firm in same industry . Old and new bosses know each other

I'll keep this short,I was put on a performance plan at a boutique for poor performance. Owing largely to being staffed with an asshole director who would call me all hours and hurl abuse. He broke me and I eventually resigned

2.5 years later I have managed to secure an offer in the same city with a BB

-Found out yesterday that old boss and my new boss know each other.

-I didn't leave on bad terms but I did quit while being managed out

-I haven't updated LinkedIn for fear of being discovered. I guess I could block my old team completely and then update my role but it will eventually get back to them.

-I really don't want to leave this team either, they're a great team with a good culture

How should I manage new boss finding out?

• what do I say if asked about my time there?

• since being performance managed out I have turned life around and the BB that I accepted was 1 of 3 that I was actively interviewing with

What about updating LinkedIn ( I could wait until probationary period is up and then do it).