Also, when did Sony announce the following?:
Doubling Frame Rates
Full clock speeds for ALL games
16xAF
Auto HDR
Gen 7 games
Gen 6 games
When they announced the BC and its boost mode, or when they detailed it on the PS Blog website and the PS support page FAQ mentioned that exactly like in Series X, BC games would increase their framerate when played on PS5. Obviously this will be noticiable on those games that weren't already running at steady capped 30 fps or 60fps.
In devs desire it, PS4 games capped at 30fps can be patched to add an unlocked fps mode/60fps limit, so they run at 60fps in next gen. Ghost of Tsushima announced that they did it for PS5, Fallout 76 devs announced they did it for their game (at least in Series X). If not patched or released as native next gen games with improvements, games locked at 30fps will have less and smaller framedrops on both consoles.
Same happens with resolution, in both consoles if games have dynamic resolution its resolution will increase. If instead have a fixed resolution, their resolution won't increase in next gen consoles unless they get patched with a dynamic resolution patch or an improved port for the next gen console/remaster/remake.
Sony didn't announce 16xAF or Auto HDR for BC games.
PS5 will have more Gen 6 BC games than Series X, even if not directly. PS4 had the 'PS2 Classics': some emulated games with added trophies like GTA III, GTA Vice City or GTA San Andreas, the Jak games, Bully, Max Payne and like over 50 games. Here you have a list, I don't know if it's updated:
https://en.wikipedia.org/wiki/List_of_PlayStation_2_games_for_PlayStation_4
It's a bigger list than the 42 Xbox games supported by XBO (so Series X, which its 360 ad OG Xbox games list will be -or aim to be- the same):
https://en.wikipedia.org/wiki/List_of_backward-compatible_games_for_Xbox_One
PS4 also received a ton of remasters or remakes of Gen 5, Gen 6 and Gen 7 games: The Last of Us, God of War III, Uncharted Collection, FFVII Remake, Crash Bandicoot N.Sane Trilogy+ Crash Team Racing Nitro-Fueled, Parappa The Rapper Remastered, or some were crossgen with gen 7 like Journey. Then some other gen 5 games are also included in collections, like all the Street Fighter games in Street Fighter 30th Anniversary Collection or Symphony of the Night on Castlevania Requiem just to name a few.
They won't give you for free these games if you had the original ones, but you'll get them for free if you had them on PS4 and they were improved versions for ports/remasters/remakes (or emulated arcade perfect versions instead of a choppy PS1 port in the case of arcade games).