It's a bit hit-and-miss... but basically, you 'force close' Google PlayStore and clear its cache. So, go into Android Settings => Apps => Google Play Store, and choose 'Force Stop' and then "Clear Data" (in that order). Then, come out of Settings and turn on your VPN to whichever country (e.g. Georgia), then re-open Google Play Store and hopefully it'll be in the new country.
It doesn't always work, sometimes you have to do it a few times or even "switch accounts" (within Google Play Store) as that seems to 'jolt' it. It seems to be that if you've clear PlayStore's memory/cache (as above), it forgets which country to show you so when you re-open it with your VPN on (to whichever country), it thinks "oh, right, you're in [Georgia], so we'll show you apps for that country".