It's a very niche thing you're going for. A niche subset of a niche subset.
You're playing on high, which reduces your framerate versus playing on 'competitive settings'. But you're still trying to squeeze as much framerate out as possible. Tbh it sounds a bit like mixing the worst of both worlds, where you play on neither low or very high settings, and limit yourself to 1080p.
That might be what you enjoy the most - maybe you tried 1440p and didn't like it somehow - but it's so incredibly uncommon to go with this kind of setup that it's hard to make any sensible suggestions for it.
Valorant will pull hundeds of FPS with a much weaker GPU than a 2080 ti.
Every frame counts in this competitive FPS, but hitting 144+ fps is surprisingly easy.
Apex Legends will not give a consistent 240 or even 180 FPS
Apex Legends is one of the most-watched games right now and is among the top Battle Royale genre of games. Running on the Titanfall engine and with some revamped Titanfall assets, the game is a fast-paced FPS with relatively high poly count models and long view distances. For this reason, we’re...
Moreover, upgrading from 180hz to 240hz... why.
Some of the games you're playing won't get that high in framerate. Those that do you may not notice the difference. And if you did, and you wanted the competitive edge that brings, you should probably be playing on lower setting anyway in the others games for the higher framerate.
Tbh you'll probably just buy a 2080 ti because going by the rest of your spec you seem to buy expensive things because they're expensive rather than meaningfully beneficial. And it's your money.