His TPs are absolutely good but they're the part of his identity that is most well liked and makes him fun to watch in pro. You could maybe improve clarity on them but otherwise I think it's best if TP is why you pick him.
Astra and a few other slot options can do similar rolling retreats in some spots with dissipate, so i think it should be alright overall on most maps. It's fine if Omen is still preferred on Lotus and Sunset specifically even because Astra can still take maps like Haven and Split from him, which is the main idea behind my paranoia nerf anyway, to weaken his stopping power on defense without committing to it a bit more, meaning he'll be TPing out more but not slowing hits as much.
Icebox is a very different beast entirely and I think very emblematic of the duelist-y style of play that people enjoy the most from him. The solution there is probably to look at Jett's balance and Icebox's map design, rather than Omen's personal balance, imo, although I also dont think he's particularly overperforming on Icebox so much as a good consideration to take 0.5 duelist and 2 controller on the least duelist heavy map with the most off angles in the game.
Paranoia getting traded for ults as often as it does is a big part of why I feel it needs nerfed too. Breach isn't a great example because he's very clearly underpowered himself, but having to reactively spend his 9 cost ult just to defend your team against a reclear because of one flash is fucking insane game balance and needs looked at.