What CPU cooler should I get for my PC build?

I'm looking for help picking a CPU cooler for my build. I just moved my setup to a new motherboard (specifically, the B560 AORUS Pro AX), and unfortunately, the CPU bracket broke, so I need a replacement cooler fast. My CPU is an i9-11900KF paired with an AMD RX 6600 XT, and I have 750W PSU and 48GB of RAM. I spent quite a bit on the motherboard since I switched from a micro ATX form factor, so I'm hoping to find a good cooler without breaking the bank. If you need more details about my build, just let me know! Also, can I still use a heatsink cooler, or should I consider something different?