It's been hit-and-miss. The process can be inelegant, but it's been shown to be feasible. FFVII:R, Ghost of Tsushima, Death Stranding, Crash Bandicoot 4, Greedfall, hell, even Bugsnax supports save transfers from PS4 apps to PS5.
Where it's unclear is for games that release simultaneously on PS4 and PS5, and my guess is Sony may have a hand in it due to trophies. For example, neither COD Cold War or Kena: BOS have a save transfer option, but they also released day and date on both platforms. Bethesda not doing it for a port of Quake (1996) clearly appears to be a conscious decision to not.