I recently removed my 25Gbps PCIe dual port cards from my 2 servers because they were using 20W more. My entire rack including 2 UniFi PoE connections uses 90 W now (so 110 W just for having 25 Gpbs).
There is some heat from such cards, but usually it gets transported outside fine. The ones I bought did not come with a fan. I think you cannot operate them without one. The heat sinks get very hot.
Stable is for servers, unstable for desktop. It has worked for 20 years. I actually installed two further Debian workstations recently after trying and failing with Kubuntu. So … no, I don’t have this problem.
No idea why busybox is needed. Is this is your emergency boot environment like initramfs? Sometimes it’s nice that Linux boots up and offers an environment to fix stuff while some modules are broken.