What type of breed would you say Coffee is? I have a goldfish that looks quite similar to yours. For the longest time, I've always assumed mine was a comet, but upon doing some extensive research, I believe it might be closer to a Veiltail. The reason I ask is because my goldfish has similar symptoms to yours, and I believe it might actually have something to do with the breed. My goldfish started developing visibly red veins around the age of 5. He is now 9 and sits at the bottom most of the time, except during feeding time. Mine doesn't really have patches like yours, but rather long visible red veins. However, the patch at the end of Coffee's tail in the first photo does look like some kind of burn?
This is some information I found from a post on another goldfish forum (https://goldfishkeepers.com/community/threads/persistent-red-streaks.8158/):
"The fish you have pictured are Veiltails or close to veiltails. In Veiltails older fish often get varicose veins, if it is bacterial, it is because the tissue is so thin in these big tailed fish you can try oxilinic acid. But in reality, old veils sit and some get puffy red veils, we have eliminated this by selecting for young fish that have shorter tails with a thick peduncle. If you have to breed this guy, breed it to the shortest tailed fish you have, even a chop tail to shorten the next generation.
In reality, veiltails at four to five tend to sit and look like this unless the peduncle and tail length has been selected for."
"I have hatched over 300,000 veiltails since 1985, and these veins have been a persistent issue until 2005 when we formed a breeding group to elimante them. US bred Philly descendants have lost this trait, but still get tired at 4 or 5 and tend to become tail sitters or standers"