X Mentions
Someone complaining about you in public is worth answering faster than a direct message. The X Mentions inbox polls for mentions of your account, threads them into conversations, and lets an agent reply as a tweet from the ordinary reply box.

Connecting your X app
You connect your own X developer app rather than a shared one, so your account keeps its own rate limits and permissions.

Access tokens refresh on their own once connected, so a working inbox does not need reconnecting.
How mentions arrive
Mentions are polled rather than pushed, so a mention appears within the polling interval rather than instantly.
A mention thread becomes one conversation.
Replying
Type in the reply box and the reply posts as a tweet.