HDD about to die. Which steps to take? (win10)

My non os hdd is about to die: boot takes ages, recovery is not working. I can navigate the directories but trying to access anything hangs the process. HD is still visible in the BIOS.

I've already ordered a replacement, and in the meantime I've just disconnected it, to avoid extra stress.

Short of sending it to a recovery service (that will be done as a last resort, for the few files i need that weren't backed up), what are the steps to take to save as much as possible?

Windows 10 Home, build 14393.rs1.