I would like to set "not connected" tabs to a passive color like light gray to indicate they are not actively connected to a database. Current tab coloring is set by the connection, so this isn't possible. One possible implementation is to create an environment called "not connected" and then specifying NULL in the "SERVER" field.

This would be especially helpful for those who use SSMS's dark theme with SQL Prompt, because "not connected" tabs become nearly invisible with a black background and black font.