Time Machine backup safety with unresponsive iMac hard drive
late 2012 iMac running macOS Catalina
[Re-Titled by Moderator]
iMac 27″, macOS 10.15
Your Time Machine backup resides on an external drive that operates independently of the iMac's internal drive. If TM was backing up your computer properly before the internal drive failed, your backed up files should be unaffected. Since the iMac is not working properly now, just disconnect the TM drive and put it aside until you get the iMac repaired or replaced. When you have a working Mac you can restore your files from the backup drive and carry on.
Restore items backed up with Time Machine on Mac - Apple Support
You can make a Genius Bar appointment for hardware/software service and support using this link:
Contact Apple for support and service - Apple Support
Get your Mac repaired and see how much will it cost:
Mac Repair & Service - Apple Support
Call Customer Support (800) MY–APPLE (800–692–7753)
or on line https://getsupport.apple.com/
or call AppleCare Support at 1-800-APLCARE (800-275-2273)