A Noctua NHD15 is still more than capable of cooling pretty much any CPU out there, especially AMD, and especially especially the new 9000 series which apparently run surprisingly cool. Other air cooling options are available. People also like the Thermalright Peerless Assassin, Deep Cool Assassin 3 or Sycthe Fuma all of which are cheaper. Noise wise, they'll probably be fine in a case sat on the floor.

Short answer: I wouldn't worry about air cooling a CPU unless your going to do some kind of mad overclocking or breaking benchmark records or something.

A lot of 4080s use the same heatsinks as the 4090s so they should be very quiet. I have a gigabyte OC 4090 and I have it undervolted as far as it will go (200 watts typical, 300 watts max) and I can't hear it in my fractal define R4. Undervolt your 4080 a smidge and it will be dead silent. My CPU is a 5800x3d with an NH-D14 and it's not possible to hear that thing.

Also just FYI the R4 is not large enough for the 12vhpwr cable, you have to make too sharp of a turn radius for it. My 4090 is undervolted so far I'm not concerned, but be aware of this.

Buy an X870 board for future CPU options, buy whichever 9000 processor that you settle you, after CES buy a 50 series from nVidia, they'll have GDDR7 and could be slightly thinner, set your fan curve in UEFI and GPU software, look at a Dark Rock Pro 5 for CPU, and you can get it pretty silent.