[Bug]: Chat overrides the "Enter" action of alt-f4 exit game menu

### Describe the Bug

When the game ends and I want to exit quickly, I press alt-f4 then enter, but enter brings up the chat menu instead.

### Reproduce the bug

Open the exit game dialog with escape or alt-f4 or exit game button, then press enter.

### Screenshots

_No response_

### Additional context

_No response_

Reproduce the issue by opening the exit game dialog with Escape or Alt-F4 and pressing Enter, then trace the chat and exit-dialog input handling in the Lua code. Done means Enter confirms the exit action without opening the chat menu.

Written by the indexing model from the issue text.