Yes, your PS4 can download games in rest mode — here's how to do it

A PS4 can download games while it's in rest mode. PS4 games can also update while your PS4 is in rest mode.

How to upgrade your PS4 games to play on a PS5 with better graphics and frame rates

You can upgrade eligible PS4 games to play on a PS5 in higher quality through the PlayStation Game Hub and PS Store.