Okay, it was easier than I thought.
The solution that worked for me was to add a very simple /etc/wsl.conf:

enabled = true
options = "metadata"

I found part of the answer at Stack Exchange's Super User site:

... but that answer resulted in fixed directory permissions and ignored file permissions for me.

I read the referenced MS page:

... but using that code resulted in not mounting the host drives at all. Using just the enabled and options parts from the page resulted in fixed directory and file permissions, which kinda works, but I'd rather set the permissions myself.

Then I remembered that the temporary solution from here only sets the "metadata" option. So, that's what I did, and it works like a charm... Just like I have a real operating system with a real filesystem.