The trouble with maintaining f.lux is that we do feature updates sometimes, but we do compatibility updates often as we're glued between the operating system and a bunch of third party drivers. If we had to explain to each person why they should update we would be having millions of conversations about it all the time.

"Update f.lux automatically"

to disable "Update f.lux automatically" does not prevent this update nag popups. "Skip" Button has no function.

I'm sorry to have to put it so drastically, but this behaviour of software reminds me of crap- or malware.
Unpreventable telemetry and non-functioning "skip" buttons and settings that don't do what they say they do.

Turn off "Update f.lux automatically" in its settings.

Or, uninstall it and then reinstall it through Microsoft Store. That way, updates will come automatically just as they do for all other apps installed via Microsoft Store which means you'll never again see any messages about the updates.

If you "skip" an update it will not prompt you for the same version again, but it will prompt for other versions.