Lots and lots of “don’t do it” talk out there but others report no problems, having done it for years. I believe it’s totally doable.

Use Mailu for server ? or Docker Mail Server ?
all email from ImprovMX goes to Mailu server
NextCloud mail client connects to Mailu server

Does outgoing mail need to be routed through a service that eliminates the “mail server reputation” issue? If so, which one to use?

Run Mailu on its own (thin client) machine?
Or coexist with NextCloud?
Ideally on a Kubernetes cluster but initially, maybe a Docker swarm?