The rear derailleur skips on the third gear when I push hard.
Cable tension first: a quarter turn on the barrel adjuster while pedalling usually finds it. If it only skips under load and shifts cleanly otherwise, suspect a worn cassette paired with a new chain, which no amount of adjustment fixes.
Which mini PC is quiet enough to sit in a bedroom?
Anything fanless with a passive case, or a laptop-class chip undervolted and capped below its turbo. The noise people actually notice is not the fan at load but the pulsing at idle, so a fan curve with a wide hysteresis matters more than the rated decibels.
My desk wobbles at full height. Anything short of replacing it?
A cross brace at the back removes most of the sway, and moving the heaviest item to the centre helps more than it should. If the wobble is front to back rather than side to side, the feet are the problem and shims fix it in five minutes.
Is there a simpler version that gets most of the benefit?
Yes: do the first step, skip the automation, and revisit in a month. Most of the value is in the first step, and most of the cost is in making it repeatable before you know it is right.