[EPM] Better error handling and logging

[neptunian]

• what errors to log using Logger
• what kind of errors to throw in API responses ([EPM] handle unremovable packages #64096 (comment))

#64809
#60952

[elasticmachine]

Pinging @elastic/ingest-management (Team:Ingest Management)

[skh]

I've learned that Cloud users can't see Kibana logs, so we shouldn't put any information there that they would need to handle problems.

[skh]

Closing in favor of #66688