TLDR: While Fediverse won’t directly serve you ads, anonymous bad actors other than Meta can save, redistribute, and even dox you for any information you post here. Anything you post here can/will remain forever on some malicious instance that doesn’t honor deletion requests. So be careful!
Anything you post on the internet is public and you should stand behind it. If you want to be anonymous on the fediverse there’s steps you can take to make sure you aren’t easily doxed. use a unique username and email thats not used anywhere else. don’t post photos that can possibly be geo located. Don’t mention who you work for, don’t mention places you visit. Pretty basic stuff.
Treating any online interaction as a public forum is best practice. I wouldnt say anything online I wouldn’t say in public.