First off lets get one thing out, there are legitimate used for every type of connector! Personally I've not used WAGO's, simply due to having other solutions that work. I would not go out of my way to buy some for anything planed at the moment.
Does anybody use wago connectors (or some other type of pressure connector) for prototyping or building their project? I'm working on micro-controller projects and during the initial testing and programming phases being able to attach/detach components is quite useful, but sometimes a breadboard isn't terribly convenient.
At times breadboards can be hell so I understand. What is the best solution really comes down to what is being done. Ideally a breadboard should be mounted on a plate and frame so that commonly used devices can be mounted adjacent to the bread board. The first item here would be binding posts/banana Plug sockets for secure connection to power supplies, and meters/instruments. There is nothing worse than scratching ones head only to realize that a long lead pulled a wire out of the bread board. The idea here is that a banana socket is far more secure for a DMM connection than a wire and alligator.
More along the issues that you are trying to address with Wagos it might be better to also mount a DIN rial to the plate and snap on a few similar DIN rail terminal blocks. The same logic applies here, the idea is to have an interposer between the breadboard with the delicate connections there and the off board world. The goal is the same, to keep things from being pulled out of the breadboard. Also having a DIN rail ready to go allows mounting a massive array of stuff from other manufactures. In any event if you have a lot of projects planned where you have many external devices that you don't want creating problems at the breadboard, it is nice to have a solution that prevents tugging the breadboard. There are other similar approaches that don't involve DIN rails. In any event there are dozens of suppliers of this sort of technology, you can find a block for almost any need.
Do these connectors work well with small gauge wires? They say they work from 12-24 gauge. Most of the wires I have currently are 22. Do those still get a good connection?
Working and trouble free are two different things. Some of these spring connectors have a bit of a death grip that is not ideal for small wires. However most terminal solutions are so encumbered, the reality is fine wires break easily. This is where wire ferrules are a life saver for small diameter wires. I'd suggest that getting a ferrule crimper should be high on your priority list if you are using any sort of spring clamp or set screw type connector in conjunction with small diameter wires. This especially if you want reusability. This is one reason I wouldn't jump at these sorts of Wago connectors, they are more designed for electrical wiring. With the DIN rail components or similar direct mount devices, you have all sorts of blocks available.
So again I don't want to completely dismiss these connectors I just wanted to point to alternatives that might make more sense. The idea to have a few banana jacks available for example can solve the problem of instrument leads or power supply leads, pulling out of a breadboard. If you get on a DigiKey or similar web site, there are literally tens of thousands of ways to make up connections to help with prototyping. I don't want to suggest the more questionable ways but I've literally have used alligator clips to kee two wires together. Use what you have at the time.