The E-cores (on existing Intel chips) aren't going to help with gaming ever, there's just too much latency communicating between them and the P-cores. That said, performance is similar to AMD with Raptor Lake often slightly edging out Zen 4, albeit at higher power usage, but this can vary game to game. Until Cities Skylines releases and we have third party benchmarks, it's hard to say which will be better, but they should be close either way. Raptor Lake refresh is also about to release which will probably add another 5-10% single threaded and a bit more multithreaded performance.

I don't know where you got the idea that they aren't detected correctly. Intel and Microsoft worked together on the thread director for Windows 11. There were some teething issues in some games and apps early on but it's been 3 years and most of the biggest issues were fixed in the first few months. They even work decently well on Windows 10 (I have a 12600k on 10). You can also disable them if you run into any issues.