That’s already the case (see above “whitelist”).
If you are using data saver, make sure K-9 is also exempt from that.
Depending on your Android version, you can pick either “may use data in background any time” or “may schedule background synchronisation”.
No, wasn’t using data saver either.
Somehow it started working now, without me knowing why. I went through all the settings without changing anything, I just unchecked and checked some checkboxes again, also inside my e-mail provider. But can’t reproduce what made it work now. But it’s working now, that’s positive at least.