Pop-out chat and an OBS chat overlay
Open your combined chat in its own window, and add it to your stream as an overlay with a private OBS browser-source link.
Pop-out chat
The chat rail’s pop-out button opens your chat in a separate window, so it can sit on a second monitor. The window keeps up with new messages. If you scroll back, a “new messages” button takes you back to the latest.
Chat overlay for OBS
The Broadcast page gives you a private chat overlay link to paste into an OBS browser source. The overlay shows chat only, with no controls. Add ?bg=transparent to the link for a transparent background. Anyone with the link can view your chat, so you can regenerate it at any time and the old link stops working.