I have a 30-inch Apple Cinema Display connected to an OWC Thunderbolt 3 Dock with a Dual-Link DVI to Mini DisplayPort adapter. I’ve been using that adapter and the dock since 2016 to run the 30-inch Cinema Display with a MacBook Pro (it’s the first-generation of the MacBook Pros with Thunderbolt 3/USB-C ports). This setup has worked great. I recently ordered an M1 Mac Mini and a Pro Display XDR to upgrade. The M1 Mini arrived today. The XDR display is still about six weeks out, but I thought I’d go ahead and set up the Mini and just use it with the 30-inch Cinema Display until the XDR display arrives. I assumed I’d just be able to unplug the Thunderbolt 3 cable from the MacBook Pro and plug it into the Mini, and it would work fine on the 30-inch Cinema Display. It does not. The best resolution the M1 Mini will produce on the Cinema Display is 1280x800. It looks awful and is essentially unusable. The MacBook Pro has no trouble running the Cinema Display at 2560x1600 with the exact same adapters, cables, dock, display, etc.
I just discovered this a couple of hours ago, so I’m not sure if there’s a fix yet. I spent some time Googling and hunting around to see if there are some settings I can use to fix the problem. It doesn’t look promising, but I guess it’s possible. It looks like other people have had luck with different iterations of the Cinema Display using a Mini DisplayPort to USB-C dongle that appears to be available on Amazon for about $35. I guess that might work with my 30-inch Cinema Display, but I’m not sure why it would be an effective solution if my OWC Thunderbolt 3 Dock is not. (The distinguishing feature creating problems in my case, and what I assume would be your case, might be the presence of the additional Dual-Link DVI to Mini DisplayPort adapter that you need in order for the 30-inch Cinema Display to work with a Mini DisplayPort connection at all. The people who had success with the $35 dongle might have been using newer Cinema Displays that have Mini DisplayPort connections to begin with, rather than Dual-Link DVI like the old 30-inch Cinema Display.)
As for me, I’m not going to spend much more time (and certainly not more money) trying to solve the problem. I’ll just keep using the MacBook Pro until the XDR display arrives (which I understand will work with the new M1 Mini but NOT the MacBook Pro, haha). Based on my experience today, if I were you, I would NOT be confident you’ll be able to get your 30-inch Cinema Display to work with an M1 Mini. Part of me wants to complain, but then I remind myself I’ve gotten sixteen years of absolutely outstanding performance out of the 30-inch Cinema Display, which is more than I can say about pretty much any other piece of computer hardware I’ve owned.
I hope this is helpful, and good luck!