The only PII the software itself stores are usernames, bcrypt hashes of passwords, JWT session tokens and, if the admin requires it or the user gives it voluntarily, emails. With this in mind, there are still important caveats to keep in mind.

First, there is no way to verify if a given instance is running a fork that collects more information than the upstream repo, not to mention any logging they might be doing. This is where Lemmy being self-hostable is a double-edged sword. On the one hand, if you have the sysadmin knowhow or know someone trustworthy who does, you can setup your own instance that you can be certain doesn't collect any data you don't expect it to. On the other hand, there is no way to prevent malicious actors from making compromised instances.

The other important caveat is that all posts and comments are public. Personal information you post in posts and comments can be used to identify you. This is true of all social media, even ones that don't use usernames such as 4chan and similar chan-like image boards. No amount of software related privacy features can save you from bad opsec.