For gaming, your number 1 performance boost will always be the gpu. The 5800X will give you slight uptick at the single core performance is higher than 5600X, but nothing compared to performance boost buy going from a 3070 to a 3080 for example. And with prices as they are, that's why forum members always say get the gpu 1st, as that's your biggest cost. You need to really think how much performance you want, but as you said you initially wanted 4k gaming, I'd put 3080 or above, so for any hope to keep in your budget, you'll need an nvidia card at MSRP
The prices on the Nvidia website are the MSRP prices. You can only get them from one distributer in the UK(can't name it as against forum rules but google), and they are not allowed to increase the price, so they are the only gpu's you can get at MSRP. Everyone else has put their prices up. The only way to get one is via the FEpartalert on telegram(last drop yesterday, which i posted on the 3070/3080/3090 thread as saw it happen). This is by far your best option for bang for buck so to speak. The 3080 at £649 is the ideal card for your build I would say as offers best bang for buck, but non of the cards are bad. Getting the 3060ti at £369 would have been great also(not that far behind the 3070)...you could use that until you prices return to normal, or manage to get hold the card you want at a reasonable price and sell it(at that price you wont loose a lot when prices normalise, and at current prices you'll make a profit)
The 3080ti at £1049 yesterday is only a little behind the 3090 for performance..you pay for it, but I'd rather pay £200 more for that than a a 3070ti for £850/£900 from a shop
i looked at review after review before I bought my components, and everything is personal to you. When i looked at reviews I looked at the graphs etc, as at end sometimes a board was classified as good but not worth it as expensive, but price fluctuate all the time, and shop around. I bought from 4 different places.
Also, how long do you want to keep your pc for. If a long time before upgrading, then I'd get better stuff, as I'd get instant better performance now and it'll last longer before I feel the need to upgrade.
for example, with your build, I would want 32gb of ram. i know there is debate for the need for this, but with the migration to DDR5 in a few years, if I had 16gb and needed more, I'd prob have to pay up to get some, as DDR5 will be the prevalent Ram, so DDR4 will become more expensive as supply dwindles. That would in turn mean you can't get the bundle you put in there, but then the mobo you have there is more the budget end b550(from reviews I've seen...so my personal view), so getting a 3080 I'd want one that has better thermals, and also if i upgrade to a better cpu in future, I'd want my mobo to be able to handle it(it prob could but for me, I'd want something else..again, personal)
I can list a whole lot of reviews of boards if you want, but would have to be later, gotta go for present