I want a dock that I can plug a Studio Display in. It may be that they simply can't do that period. As far as I know they simply have to be plugged directly into your mac.
I have a CalDigit TS4 that I connect with one (the supplied one) TB4 cable to my 14" M1 (Pro) MacBook Pro. To that I have connected my Studio Display and another 27" LG display (4K) and that all works perfectly. I'm usually running in clamshell mode, but have, at times, used the built in display at the same time, too, and it's all handled flawlessly. In addition I have an audio interface, 2-3 ext SSDs, GB ethernet and sometimes other peripherals hanging off it.
The only problem I have had is that when I first set it up I couldn't get full resolution on one of the displays (I don't remember which, I probably doesn't matter). That turned out to be because the cable I was using wasn't up to spec. After replacing the cable I've never had a problem.
... On that machine, at least ...
I also have a 16" M2 Max MacBook Pro that I use for work. That has some AV and Auditing services on like ZScalar and Crowdstrike. I suspect it is a result of that, but I can't get both displays to work via the dock on that machine. But if I connect one directly then it *does* work.
So if you're having issues that's two things to look for, based on my experience: 1. Make sure your cables are good enough (at least TB3) and 2. If you have any corporate monitoring tools they may get in the way.