Some other apps are often willing to accept my current setup (Lineage for microG [0], plus Magisk, if you don’t need root – Magisk Hide does some magic I don’t really understand, but even without Play Integrity passing, apps just start working).
With more tweaks, you might be able to get Play Integrity to work to some extent, but it’s hit or miss. I’ve just stopped using apps that demand it.
Even un-modified you'll then be stuck with an old version of Android that doesn't support the latest versions of apps and the old versions of apps won't work properly.
It's really a shame because a lot of old phones work perfectly fine otherwise.