When you upload an APK, it must meet Google Play’s target API level requirements.
Starting on August 31, 2023:
New apps must target Android 13 (API level 33) or higher; except for Wear OS apps, which must target a version between Android 11 (API level 30) and Android 13 (API level 33), inclusive.
App updates must target Android 13 or higher and adjust for behavioral changes in Android 13; except for Wear OS apps, which must target Android 11.
Permanently private apps—which are restricted to users in a specific organization and are intended for internal distribution only—aren't required to meet the target API level requirements.
minSDK dictates if an app will work on your old device or not. Depending on how you build you app, the minSDK can be 14 (Android 4), 19 (Android 4) or 21 (Android 5). Google Play services do not support Android versions below SDK 19
targetSDK is simply the way for the developer to say "my app works best with this SDK version and I want to use the new features"
As long as your device has an higher version than the app's minSDK the app will work. For example, if the app's minSDK is 26 (Android 8), the app will only run on devices with Android 8 or higher.
This also means making your app work with the new features, so e.g. you may need to implement a flow to request certain permissions that you were previously getting automatically.
I get that it’s up to the devs to authorise it. It just seems odd that they seem to require manual review for some apps and others is just a minimum. Perhaps it’s a setting.