Baking inherently takes time, so I can't help with the desire to get from a cold start to baked goods in twenty minutes, but I've been doing more baking (especially bread) over the last several months while stuck at home, so I can offer some tips on workflow, timing, and the mess factor.
First, about the mess from flour and sugar: this got a lot better for me when I got a kitchen scale. Scales small enough to keep in a drawer or leaning on the back of the counter are pretty inexpensive these days. Measuring ingredients by weight is more accurate, which is why I got a scale, but I've noticed that I have a lot less airborne flour dust and suchlike because instead of scooping flour out of a canister or bag several times with a measuring cup (and having to level it off each time), I can just pour flour into a bowl on the scale. Less movement means less flour floating through the air and settling where it likes. Also, I find washing a bowl easier than washing a bunch of measuring cups. (You can pour directly into the bowl you're going to mix in, which means nothing extra to wash, but you run the risk of adding too much and that's hard to back out.)
I don't know how well this works for rolled cookies, but for kneading bread, use a large board. You can then pick up the board and wash it, which I find much more effective at removing residual flour than having to clean a countertop directly. (Yes, you'll still need to wipe down the counter, but it isn't more trouble than any other post-food-prep counter cleaning.)
A bread machine can produce reasonable bread of many types and the only cleanup you need to do is to wash the pan after (and maybe wipe the inside of the lid). You can also use it to do the mixing and kneading but then do the final shaping and baking yourself, if you want to make rolls or braided loaves or something like that instead of a single plain loaf.
Some cookie dough freezes. A friend who lives alone makes a batch of 3-4 dozen proto-cookies, rolls the dough into balls, and freezes them. When she's preparing dinner she takes one or two of the balls out and bakes them. I am unsure of which cookie types work better or worse for this and how starting from frozen affects cooking time, but it's something you could experiment with.
Most cakes can also be made as cupcakes or mini-cakes (that is, using smaller pans). The cooking time will be shorter than for a cake in many cases, but you'll need to experiment.
I've found that anything that involves an electric beater and either sugar or flour is going to make something of a mess. Maybe deeper bowls would help? I do a fair bit of hand-mixing before applying an electric beater in an effort to keep the spray down.