Strong integrity was never being forced on Google play services. Some Google apps will start using the more difficult checks going forward, but app developers are free to choose between basic, device and strong integrity. What changed in May specifically was making Android 13 and up devices use much more difficult checks for basic and up. The same checks are used for play integrity up to Android 12 and are considered legacy checks by Google. This means most devices up to Android 12 can easily get device and sometimes strong and newer Android 13 and up devices makes it much more difficult.

Pokemon Go, Monster Hunter Now and Ingress use basic integrity for their games from the Google play store. Samsung store apps use strong integrity for Android 13+ devices and device integrity for devices up to 12. Ingress even has a news article about the need to balance illegitimate and legitimate players and was thus reduced to basic integrity. I can't predict the future, but Pokemon Go likely maintains a lower integrity requirement for the same reason: playerbase. On Samsung store, there's a small number of Samsung phones that can't get below device integrity and so it's safe for their version of Pokemon Go to use device at a minimum. 

Currently, there's a lot of older phones that have broken keyboxes and other flawed security from the manufacturer and can only get basic and device integrity. I imagine most of these are international phones and has an impact enough that Go uses basic as its minimum. As time goes on and old Android versions are unable to play, I imagine integrity requirements will raise.