Repairs take a long time, and you can't improve the speed of repair by putting on more plants and construction yards - the speed of the repair is limited to the speed at which construction yards can place components on the repair target since component plants build components far too rapidly for the yards to keep up, assuming there are sufficient resources to do so. Only one yard will work on building or repairing the target ship/station, so don't place more than one thinking it will help. You also don't need too many cargo bays, the my biggest stations sizes are 3000-4000 and never need more than 8k resources and construction ships go back to planets each time in order to resupply with necessary resources. Technology does improve the rate at which components can be added, just look at the construction rate of the construction yard. From my experience, repair rates are slower than building rates as well, when it comes to component placement.
So when it comes to repairs, make sure you have plenty of construction ships. Not too many that you're wasting so much money on maintenance, but enough to continually construct gas/regular mining stations, resort bases, tech labs at research bonus locations, and then at least several construction ships for repairing both your own damaged ships and those found in special locations. However, when it comes to repairing your own ships it may be more convenient to scrap it and just rebuild it at a shipyard. You'll pick it up as you go. Monitor your construction ships' statuses through the bar on the left (by the way, this is super helpful for making sure all your assets are hauling their weight in productivity, like colonies, spaceports, exploration ships, and for listing good places for research/ resource extraction), and you'll eventually get the hang of it.