places an undue burden onto the user to determine and explain why data might be personal
The other way around: all data originating from a person, is by default "personal data", and the burden of explaining which one is not, lies with whoever is keeping it.
you can't look at any messages in any rooms you've been kicked out of
If they're keeping them, then you can request a GDPR export of ALL your data. Doesn't matter whether some interface or application allows you access to the data or not, or even if you've been banned from the whole platform; as long as they keep the data, they have an obligation to honor your rights of:
Access
Correction/Modification
Removal
Even during obligatory data retention periods, when they can't remove the data and only make it inaccessible, you still have the right to get a copy of your own personal data.