I did notice that it wasn’t sleeping properly, so I just SSH in and kill the offending process as needed. The issue only comes back following a restart, but otherwise the HDD works great. The disk is asleep unless I am actively backing up or using it.

I also have an offline external SSD I use as a redundant backup to be safe.

My router has a USB port and supports time machine backups over Wi-Fi. I just connected an external hard drive and it works very well. It ended up being the easiest solution for me without needing to invest in a whole NAS.