I don't have any flickering issues with my setup. My monitor is a Thunderbolt display and I am using the Thunderbolt cable the monitor came with.

My experience with issues like that are usually the cable. It may be worth trying a new USBC/Thunderbolt to DisplayPort cable, or HDMI cable? I've always had good luck with Cable Matters.

It sounds like you will need a Thunderbolt dock, unfortunately there just aren't enough ports on the MacBook Pro or MacMini. This would actually make your laptop situation a lot easier and cleaner. The CalDigit TS4 is the best option out there, but it is expensive and hard to find. There are also docks that, based on appearance, are all likely the same under the hood: Kensington, Sonnettech, for instance. Some Thunderbolt 3 stuff doesn't play nice with M1 Macs, so be sure to do your research.

Hope that helps!