> As an update, I am attaching my current .emacs.  Interestingly, it
> does not set C-x for the entire session, but if I eval-region on the
> overriding-local-map chunk, then it takes. Is the overriding-local-map
> so local that it won’t work in .emacs?

I was able to reproduce the issue as described on macOS with the .emacs
provided, and reduced it to the minimum as follows:

(define-key global-map [(control ?\])] 'Control-X-prefix)
(make-local-variable 'overriding-local-map)
(setq overriding-local-map (copy-keymap global-map))
(define-key overriding-local-map [(control ?\])] 'Control-X-prefix)
(global-set-key [(control x)] 'next-line)
(define-key global-map [(control x)] 'next-line)
(define-key overriding-local-map [(control x)] 'next-line)

(custom-set-variables
 '(global-tab-line-mode t))

The culprit here is global-tab-line-mode.

Commit 230eecf12a introduces C-x prefixed bindings for tab switching,
which are present in 30.2 but not 29.4.