I think if you just mention them all in a private mention, clunky for sure. irc used private channels only accessible to mods. not sure if that's any help but most of my groups don't need much modding. public mod log notes all mod actions. I like that it is public so there is not much behind the scenes drama to gum up communications. profile histories are the quickest way to see where someone is coming from.

Lemmy doesn't have an integrated mod mail system. You have to ask the other mods to create accounts on a chat service like Matrix or Discord, and hold group chats there.

As a side note, having a Matrix account can be helpful in general on Lemmy. Several instances have open group chats on Matrix where you can report issues or ask questions of the admins. There is also an overall Lemmy space on Matrix: https://matrix.to/#/#lemmy-space:matrix.org

Not natively. You’ll have to set up a discord or something else external for a real time group chat.