Re: CC Mode 5.31.3

[Richard Stallman]

    The issues with the Mode Name, and minor mode flags in the mode line are
    still unresolved.  On typing M-x smerge-mode, C Mode's flags (the "/la"
    of "C/la") now stay with the major mode, but this is done by setting
    mode-name to "C/la", a stop-gap solution at best.

I do not understand "now stay with the major mode".
What does that mean, concretely?

Anyway, can't you achieve what you want with a local
binding for mode-line-modes?  Or mode-line-process?