Unless you have a specific reason to use Google Play Store (as in the app, not the distribution medium), I would highly recommend using Aurora Store (which you can handily get via F-droid). I use it on my Sailfish OS phone (C2) to similarly get apps not available via F-Droid.

https://f-droid.org/packages/com.aurora.store/

The problem with this approach is that many "secure" apps nowadays (bank, authenticators, etc.), at least here in the Nordics, are checking (among other things) if the app has been installed from the Play Store. If you install the very same signed APK from Aurora, or another source, it will refuse to work.

That's probably better for the sanity of all concerned. I'll have a look.