No harm in installing a larger panel in the garage, but as stated you will be limited by the breaker size at the main.
It has been discussed before, but do you need 200 Amps to the garage? Is this a one man shop? How many tools will be running concurrently? I have a 30x50 garage with lift, IR compressor, welding gear, etc and 100 Amp has been fine. Now if you are going to AC and/or use electric heat, perhaps.
Clearly there is another panel somewhere, looks like on a 50 Amp breaker. Where is the white or neutral for that run? It looks like there is only an unsheathed ground, and I suspect there are 120V circuits wherever it is. How long ago was the panel installed?
Good thing you are only running 20 feet, you will choke at wire prices to handle 200 Amps, if you go that route.