Users DM the bot to reach your staff, and staff answer with /reply.
Members send your bot a direct message, and the bot posts it in your staff channel with a mention of the member and their user ID. The member gets a confirmation that the staff team received it.
Staff answer with /reply, picking the member and writing the message. The bot sends the reply to the member as a direct message and posts it in the channel, so the rest of the staff can see the message was answered. Only members with the Manage Messages permission see /reply.
Open one to see its blocks.
Create your bot in Kite for free, then add Modmail from Templates in your app and change anything you like in the editor.
Get started/reply tells the staff member right away, for example when the member turned off DMs, so nobody waits for a reply that never arrived.
Yes. The message posted for the staff and the confirmation the member gets are normal blocks, so you can change their text or turn them into embeds in the editor.
Everyone with the Manage Messages permission can use /reply, and you can change that per role under Integrations in your server settings.

Build commands by connecting blocks, or describe them and let AI build them. Kite is free to start and hosts your bot 24/7.