The 11900K (at least prior to the new releases) was still among the top 20 fastest CPU on the market. It is essentially a binned i7 that will for sure hit over 5GHz. It has options to unlock power draw and so forth that IMO have not been worth the added heat production in my use case. I am using one with a 240 AIO, so your 360 should do fine. You will want a Z series motherboard with robust VRM and a case with good air flow. I think the biggest complaint against it is the lack of cores/threads in comparison to the 10th gen i9.
I was able to pick mine up through MicroCenter at a starting price of $250-ish, but had a promotion/coupon that brought mine down a bit from that. I see mine running at anywhere from 4.8-5.3 on game loads based on how many cores it is using. With the "stock" power parameters set on the Z590i it is paired with I generally have idle temps just around the low 30's and in game or on load temps into the low 70's. When I go with the unlocked 250+W power parameter I cannot keep the CPU cool enough in my current configuration. I will say though that turning that on bumps perf quite a bit more even than the stock clocks.
In my own case I had purchased the 11600K at release and where it was a decent performer, just didn't have enough cores/threads or speed to utilize the way I wanted for my main gaming rig. I already had all the other components. Picking it up for cheap to update that system made sense at the time, for the price. Personally, in spite of owning one, I wouldn't recommend it over some of the newer options unless it was at an incredible price. The aforementioned Micro Center was recently doing what was a well received deal along with a mobo for about what you mention price wise.