I am unable to change Country/Region in the App Store from Poland to Russia

Apple services are not currently available in Russia due to the international sanctions in place.

There is not even a “change region or country“ button

● If an app or feature on your device is not working, not appearing, or is restricted (grayed out), a frequent reason is it may have been disabled using Screen Time, or by an IT administrator if you are using a device owned by an employer or educational institution.

- Read this support article If your Apple ID or other options are greyed out in Settings —> If your Apple ID is greyed out in Settings - Apple Support

Tap Settings > Screen Time > Content & Privacy > scroll to Allow Changes and turn on.

I can't find a statement from Apple about the availability of its services in Russia. Reading third party sites says that indeed, some have been suspended, but others are still available and isn't like Russia has entirely vanished from Apple's perspective. To me your issue of not even being able to change country settings suggests it isn't an issue because of service availability. From what I can tell you couldn't even change your account to a non-Russian country even if you wanted to.

You are correct, when you change your Apple Account country or region, some types of content might not be available in your new country or region. You will have to re-download any content you want to use in the future.

As stated, Apple services are currently not available in Russia, so you won't be able to use those services.

Before you change your region, make sure you have all the requirements ⇢

Change your Apple Account country or region - Apple Support