Game released in 2021 will run almost the same on Pro as on basic PS5 sans small boost from overclocking if turned on
Game released in 2025 will run significantly better on DRS/fps front as it will utilize better GPU
There are 4 stages on Pro transition:
1. Full compatibility - performance of Pro is the same as performance of basic model. It a base scenario for 2021 game
2. Boost mode - it's a base model with overclocked CPU/GPU. It'll give some performance boost, but not that much. This mode was manual on PS4 Pro with disclaimer that there might be issues (and there were, seldomly, that you had to turn it off)
3. Native Pro mode - it's unlocking extra CU on Pro, same as switching on better GPU, games will fully utilize extra power (PS dont switch to this mode automatically all older game as it could bring a lot of issues), but no extra features as they require explicit implementing
4. Enhanced Pro mode - devs implements features not present on basic model into game, like CBR on Ps4Pro and PSSR on PS5Pro
Stage 3 is required for all 2025 games, stage 4 is optional