The 7800X3D is the fastest gaming CPU in existence, and it can be cooled by a low end air cooler. It's the better buy than the 7700X, unless you want to save (I'd much rather save on a CPU cooler though!). For gaming, the 7800X3D is so much faster that it'd likely keep you going for one additional generation without a need to upgrade, when you think specifically of gaming use cases. Both are almost indistinguishable for productivity.
If you go with AMD AM5, you won't need liquid cooling at all. Even the Ryzen 9 can be cooled by a mid-range air cooler and perform about the same as with the best liquid cooler, making fancy cooling a waste of money.
I'd get the Noctua
NH-D12L (the bigger ones don't seem to fit in your case, but if they do, get the freaking D15S!). You'd be safe with any CPU up to Ryzen 9, and air coolers just work forever, with no funny business. Plus you will be able to move it to a future build since Noctua supports their coolers with mounting kits if needed. Which is why I'd spent on the Noctua - it could last you more than a decade, while liquid coolers are typically much more short-lived (sometimes in a destructive fashion, though they have improved a lot).
You can definitely consider a cheaper GPU - I don't think the 7900 XTX is a good buy. If you want to save a lot and still get a great GPU, last gen AMD (6000 series) are where it's at. The 6950XT is a steal!
GPUs are also the easiest to upgrade later once the need arises. Likely the GPU market will get less crazy by then.