Adding CoreProtect seems to disable the hover event on the vanilla teams prefix/suffix system. I'm assuming that this is a paper issue but I'm not sure where to start on debugging that, just that it's replicable with CoreProtect and paper alone.

paper-1.16.5-786 (Also tested on paper-1.17.1-231)
CoreProtect 20.1
openjdk "16.0.2" 2021-07-20

Logs and images without CoreProtect and the hover event working on player join, player chat, and advancement announcement.
Logs

Logs and images withCoreProtect and the hover event working on player join and advancement announcement but not working on player chat.
Logs

Simplified version of the suffix command used and steps to get it to appear.

Set use-vanilla-world-scoreboard-name-coloring to true in paper.yml then run these commands.

/team add <team>
/team join <team>
/team modify <team> suffix [{"text":"\u2463","color":"red","hoverEvent":{"action":"show_text","contents":[{"text":"TestMe!","bold":true,"color":"dark_aqua"},{"text":"\n"},{"text":"Can you see this?","bold":false,"color":"gray"}]}}]

I'll need to perform additional testing. However, CoreProtect doesn't touch anything relating to the team/scoreboard system.

A bug report may need to be submitted to Spigot or Paper. Please test with Spigot, and see if the issue is replicable there.

I had similar issues yesterday when developing a paper plugin. CoreProtect listens to AsyncPlayerChatEvent which on a paper server is considered legacy. Just having a registered listener for the event is enough for paper to have to handle legacy stuff I think, even if it doesn't modify the message and has monitor priority. Legacy text formatting does not support hover events which would explain the problem in this issue.

A possible solution could maybe be to not listen to AsyncPlayerChatEvent on paper servers and instead listen to the paper AsyncChatEvent variant.