If it does work fine without Google Play service, then there's not much you can do with this kind of pop up other than modifying the APK (or perhaps using some kind of hook framework like Xposed).
You could try something like microG, but your ROM would need to support signature spoofing.
FWIW some of the Plasma Mobile apps are available as Android apps, but I my experience most of them are not really stable enough for daily usage.
If you are looking to run the whole Plasma Mobile stack, you could use Termux and
proot
to run it "natively", although I imagine it would likely be a huge pain to get anything working reliabilly, if at all.