GDPR guarantees a right to privacy even on work devices. I think you need to filter out personal messages if compliance requires logging.
As much as I prefer the European way of some items. I think the American way of treating the work computer as a company asset and just locking it down to an insane degree makes way more sense. Especially for areas like finance.
Not to forget many constitutions enshrining privacy of correspondence which extends to emails and instant messages. Lot of work done to poke holes on it but generally it still holds somewhat in many countries.
Which is actually a good reason for entities subject to GDPR to forbid use of personal messaging apps on work devices... (And to forbid users to use work / official apps for personal messaging.)
It provides a right to privacy if the company allows personal messaging services on the device, but I don't think it provides a right to having personal messaging apps on the device(s).
Personally I think it's much cleaner to keep work stuff on your work device(s) and personal stuff on personal devices. The only place that gets sticky is where companies don't provide the device but want you to have work information on it (e.g. mobile phones)