Time Machine backup backup disc on a Mesh network

It would be best, to connected an external hard drive directly to the iMac for Time Machine backups.

see > https://support.apple.com/guide/mac-help/types-of-disks-you-can-use-with-time-machine-mh15139/mac

and > https://support.apple.com/en-us/HT201250

+1 Time Machine is designed to connect directly to the Mac. I would not risk attempting to backup over a network no matter how cool it sounds. The reason being is it will fail when you need it the most, that's just a Murphy's law.

Yes if you use a Time Capsule or supported NAS. Problem is that, neither are as fast or reliable as a Time Machine backup drive that is connected directly to your Mac.