You are correct, Target Display Mode will not work with the M1 Macs. Even if you had an older Mac as your source, it doesn't work with the Target Mac on Catalina.
There are other options, such as Screen Sharing, and third party solutions like Luna Display.
I'm reading some articles on using Airplay between the two and it seems some people have gotten that to work. But I've had no luck.
Not sure about AirPlay, but have you tried Screen Sharing? It is built into the OS.
I screen share to multiple Macs daily, even Macs with no displays attached. I screen share multiple Macs from one Mac at the same time, and even daisy chain screen share with multiple Macs. I use it with multiple different OS versions, from very old to Big Sur.
It works great for me, but does have a few limitations.
Not sure why this wouldn't work for you.
The downsides is the trade off of latency vs quality. There is a setting in the Screen Sharing app that allows for full quality, but at the cost of latency. The default setting is better latency (it is called Adaptive Quality).
Having a wired connection would improve everything a lot.
Depending on what you are doing with your Macs, Screen Sharing might work for you.