I know it’s not what you asked for but i think you would enjoy the doom games, specifically eternal but 2016 is also great.

It has great campaign, great music, arguably the best combat system in a shooter game, it’s highly replayable, 20€ with all the dlcs when on sale and when played on higher difficulties it becomes extremly technical.

It also has a multiplayer mode but i don’t know too much about it

If you want a shooter i suggest marvel rivals, it has in-game tournaments that you can access after you reach a high enough rank in ladder.

If you want a moba league of legends should have something similar in the client although i don’t know too much about it.

If you want a fighting game then you have hundreds of options. Tekken 8, street fighter 6 and guilty gear strive are the more popular ones with weekly tournaments online. (Most of these should be on sale because of the EVO which is the biggest tournament in the community)

Even mario kart wii (and the newer ones) have regular tournaments with very competitive scenes. Ultimately it’s about what you like to play and how good you are at it.