Frequent disconnections on Mac displays

Your M1 MacBook Pro supports using hardware video output to connect a single external display.

That does not mean that you can use a 24" M1 iMac as a hardware display. (Please review carefully the Support article on Target Display Mode, which clearly states that neither of your Macs support it.)

My guess is that you are using AirPlay to Mac, and streaming video over your home Wi-Fi or Ethernet network. I don't know if AirPlay to Mac would make any use of a Thunderbolt connection at all, unless the Thunderbolt link was set up as a networking link (IP over Thunderbolt, a.k.a. Thunderbolt Bridge).

If video is going over Wi-Fi, then presumably it is subject to radio interference that you might receive from other nearby Wi-Fi networks, other devices that use the same frequency spectrum, microwave ovens, etc. I don't know if the expected symptoms would include the display blanking out, or "just" more artifacts and lags.

Neither of those Macs supports Target Display Mode – either in the sense of being a Target Display, or in the sense of being able to use another iMac as one. So what do you mean about connecting the two Macs to each other with a cable to "use two displays at the same time"?!?

Use your iMac as a display with target display mode - Apple Support

Are you referring to AirPlay to Mac?!? I didn't think that required a Thunderbolt cable, just a connection to the same network. On the other hand, it is a second-class method that isn't as good as a hardware-supported connection to a real monitor.

Continuity features and requirements for Apple devices - Apple Support

Mac User Guide - Apple Support

I don’t know.