[anty]

Is there any solution that does not require me to run my own email server?

I have a 2GB email server. I use POP to regularly import the mails into Gmail. This deletes the mails on my limited-storage-server.

I already pay for Google storage. I do not want to pay (more) for another email server just so I can keep all my emails forever.

Forwarding mails does not work, because Gmail quietly drops mails. They don't even put them into the spam folder.

My webhoster told me I could pay for Google Workspace. There you apparently can use your own domain. But then I have a third service I have to pay.

[NetMageSCW]

Forwarding is the right solution, but it needs to be at a lower level than a regular user style email forward - more like a DNS delivery change.

[Jolter]

Did you rule out using IMAP?

[anty]

With IMAP i need to run a mail server that stores my mails forever, right? I want to "import" a copy into Gmail and delete it on the original server.