I'm probably still not understanding the use case, so I really don't know if this would work or how difficult it would be, but...
One potential workaround/approach (ideally tested in a demo EXO tenant) would be to create a mail transport rule that BCCes a mailbox that runs mailbox rules. Or potentially BCC multiple mailboxes each with their own set of rules. There may be some limitations to this approach depending on the specific mailbox rules in EXO, such as message moderation actions.
Or BCC an entirely different application for all emails that handles business logic for all emails in cases where the mailbox approach wouldn't work (https://docs.microsoft.com/en-us/azure/logic-apps/tutorial-process-email-attachments-workflow).
There's also a way to use Power Automate to take action on an inbound email:
https://docs.microsoft.com/en-us/power-automate/email-triggers
That said, I completely agree with the original suggestion of adding additional functionality directly to mail transport rules. Doing things outside of transport rules lead to kludgy solutions and often more complicated when running on EXO instead of on-prem.