Just for reference, I use MultiMC as my launcher.

If you join a server, leave, then join on a different account, leave, then join back on the first account, then the screenshot it'll use for loading is the second account's screenshot.

Is it possible to have screenshots tied to an account or UUID? And when you join the server, it checks which account your on?

Due to how the current setup works, such is a byproduct of using the same folder. It could be reworked in the future to take in player-specific UUID if such is not difficult.