Messages sent through the console, through a function ran with no context, or as a non-player entity should be sent to Discord.

Messages sent through the console or ran by a contextless function should be sent to Discord with the author "Server". This is most useful as it allows servers to send messages to Discord from in-game commands.

Messages sent through a non-player entity should either have that entity's name or a generic name

(reworded to be an enhancement)

Right, it should not display any message if ran through the say command.

Fair point, I'll think about it

Right, it should not display any message if ran through the say command.

Then I'll reword this to be an enhancement request later, cause it would be really useful to have some way of sending Discord messages from a datapack without sending it through a player