totally get the fear of things not fitting... nothing worse than build day getting ruined because a radiator hits the motherboard. if youre worried about the arctic being too beefy, maybe check out the Corsair iCUE H150i RGB ELITE 360mm. its way more standard in terms of thickness so it fits basically any mid tower without a fight. the performance is solid for a 7800x3d which doesnt actually run that hot anyway. another safe bet is the Lian Li Galahad II Trinity 360. it looks clean and the installation is pretty straightforward compared to some others ive seen. it usually falls right in your budget too. honestly, the nzxt is mostly just paying for the fancy screen... unless you really need to see your temps on the pump head, these other ones do the same job for less cash and less stress during the install. corsair is super reliable and has that 5-year warranty for peace of mind, though the fans can get a bit buzzy. lian li is great because it has those daisy-chainable fans that save you from a massive cable mess behind the tray.

unfortunately i had major issues with the Arctic Liquid Freezer III 360 thickness in my last build. it blocked my vrm heatsinks and just wasnt worth the struggle. the NZXT Kraken 360 is honestly not as good as expected for that price tag either. i suggest checking out the Deepcool LS720 360mm Liquid Cooler instead. its slimmer, cheaper, and kept my 7800x3d perfectly chilled without the clearance headaches.