Adding function arguments to the module browser, misnamed Class Browser, is #20827.  That leaves removing the noisy icons from class and def entries (where they do not fit anyway), as the concrete appearance change proposal here.  Better to use the space for arguments.

Adding nested classes is #1612262 (9 years ago).  I just noticed that there is a 6 year old patch that needs to be reviewed.

The TextMate box has a checkmark at the current location. Having an editor know about an attached module browser and inform it of the cursor's location would be a separate issue. It would be relatively easy when code context is active.  But nested classes and functions cannot be marked until they are displayed.

A module browser, even enhanced to display nested classes and functions, could not replace code context since the latter includes nested compound statements within functions.  I think code context would be even more useful if it were to display the complete context, using as many lines as needed, instead of some fixed number.  But I have not written a patch yet or opened an issue.