Is there significance to green, cyan, yellow, blue, red left contours of the relay outline boxes?
No, those are just based on a hash of the relay url. Where are you seeing this screenshot? It should now say "connected x times"
Coracle.social/settings/relays What is the user story/JTBD/purpose of displaying “connected X times” to the end user?
It's a proxy for how many people/groups/feeds the user wants notes from use the relay. If it's used a lot, it might be worth adding the relay as inbox/outbox. Or, if the quality of the notes coming from it is low, blocking the relay (not yet implemented).