I too had the “graphics too old” error on WoW out of nowhere a couple of weeks ago, after playing it on Linux just fine for years, no idea what changed on their part. Blizzard never supported Linux AFAIK but their games usually work nonetheless.
My PC was really too old tho, almost 10 years, it still worked fine but graphics drivers weren’t update anymore and that created a lot of problems in different games unfortunately, not only WoW (BG3 for example was full of graphics bugs - pretty unplayable, even if the PC could run it at medium settings).
I was already planning on building a new one and now it’s done, just reinstalled WoW with Lutris and it works, I used the battle.net script here: https://lutris.net/games/world-of-warcraft/.
Nvidia cards on desktops work very well, you just need to install proprietary drivers.
The problem with laptops is that they’re not dedicated cards anymore but an hybrid intel/nvidia that can give you a lot of headaches on Linux, I advise against it. No idea how AMD is on laptops.
If being cheap is a priority, I suggest getting a Steam Deck, it’s designed for gaming (unlike budget laptops) and it’s a PC. You can get a docking and connect whatever peripheral you want (mouse/keyboard/monitor/TV/whatever) and it has a desktop mode to be used as a “regular” PC if you need other things besides gaming.
LTS is your problem, it has too old stuff (kernel, drivers) for the sake of stability, never good for games, especially new ones.
If you want to stick with Ubuntu, you need the normal one, or change distro as you said, Fedora is good, Linux Mint is also really good and based on Ubuntu, if you want something more similar to what you’re used to.
World of Warcraft has its own anticheat that works on Linux no problem, if Blizzard can do it why Riot can’t? It’s not that WoW has more players than LOL so it could be justified, it’s actually the opposite.