No, it wouldn't need new textures and code.
Thanks to the PS4 Pro and Xbox One X most PS4/XBO-games already use dynamic resolutions. The textures are already made for 4K-resolutions, even if the current console hardware reduces the resolution most of the time.
A game with dynamic resolution in a range of 1440p to 2160p on PS4 Pro / Xbox One X could run in solid 2160p (4K) without changing any code. A game with unlocked FPS in a range of 40 - 60 fps on PS4 Pro / Xbox One X could run with solid 60 fps without changing any code.
Additionally Sony has patented texture replacements for older games: https://www.eurogamer.net/articles/2018-10-07-sony-patent-sparks-playstation-5-backwards-compatibility-rumours-again
Not really. They don't look too blurry in 4k, but compare the PC textures in multiplat games, there's quite a difference here. The 8GB RAM has just been too small to allow real 4K textures and had to compromise. As a result, Pro/X visuals won't be beaten.
I do agree on the framerate, though
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454
List as Google Doc: https://docs.google.com/spreadsheets/d/1aW2hXQT1TheElVS7z-F3pP-7nbqdrDqWNTxl6JoJWBY/edit?usp=sharing
The Steam/GOG key gifting thread: https://gamrconnect.vgchartz.com/thread/242024/the-steamgog-key-gifting-thread/1/