When it comes to team building, I think it's much more valuable to say "this is how we operate" instead of having everyone write down "this is how I operate". The former is a mutual guidebook for everyone to work together, while the latter feels like an edict that everyone else needs to work around you.
Check for any overtly abusive behavior that requires correction. Usually rare, but worth checking.
Provide basic coaching and suggestions for working together in a healthy manner.
And most importantly: Let them know that they're expected to figure out how to operate together on their own like professionals. Managers can't be mediators for every impedance mismatch between employees.
I'm certainly not writing anything about my personal life because that's personal and, quite frankly, none of your business. I have a tragic backstory that I don't want to share with coworkers. It's my job to overcome my past and be effective and productive at work, not everyone else's job to accommodate any unexpected or unprofessional behavior, etc.
There's a whole host of instruments that more mature companies use to uncover the different working styles and professional psychologies of employees. E.g. knowing that one colleague wants just the facts and isn't interested in the back-story whereas another wants lots of context can be very useful and ultimately help one become more effective professionally.
Why not do both? "Hey folks, here's my README, I'd encourage you to write something similar and share it with everybody."