I dont think theres any way of sending raw data from your plugin to others clients, you can probarly try with what you said HTTP Service trough the Pastebin API, but if both clients have the same plugin, you can probarly place something in game.Workspace and create a folder which contains data, make both client aware of this folder, kinda like blockchain technology
If I were to create the plugin I would create a folder in ReplicatedFirst called “[PluginName]Data” and get the Team Creators name in the Session, make the Plugin save those names trough a table, Let the plugin create a folder inside the folder and name it your Roblox Name, then make the plugin reload every second to see any new data appears in others folder
Hmm. This may not be the best way but considering nobody has solved your problem yet this makes a possible temporary solution.
Whats something that IS shared across all team create sessions? The games assets!
What if you had a folder like in serverstorage or something and you add a new string value with a message inside of it. The message would be something like “PlayerName: Message” that way u can store the players name as well. When a new string value gets added to this folder you can add it as a new message.
I saw this post when you first posted it but I thought someone would’ve provided a better solution so I opted not to suggest this. But this does make a good temporary solution if it does work. Let me know if it does!
Edit: Realized yoeymeme suggested something similar, that should work.