Ah. I understand your circumstances better. Short answer - I wouldn’t deploy menu changes. That’s usually low-lift that I would do it manually.

If I was doing it in a recurring basis I would investigate creating a process to export the menu data and import directly using a custom plugin. Or create (via plugin) and endpoint to sync both environments (a bit more work).

I did this one time before for a subset of pages and admin users. There are likely plugins that do this already but you could likely roll your own just for menus in an hour imho.

I’m not the one you asked, but when I did WP work a few years ago I would solve it via a hook that was triggered on Jenkins deploy. The hook would always fire and listeners to that hook would execute migration scripts and similar callbacks. For example used it to migrate some tags to categories and vice versa.

https://developer.wordpress.org/plugins/hooks/custom-hooks/

I remember when I looked at Wordpress for the first time, like 15 years ago, and was baffled that a dev/test/prod workflow involved copying filesystem content, database content, and changing URLs that got saved in the database. I couldn't believe what a steaming pile of garbage architecture it was.

Fast-forward to last year and I'm asked to look at it again. Surely, I think, in the ensuing time somebody would have rectified the architectural stupidity. It's a wildly popular platform, I thought. Surely it can't still be so terrible...

Fool me twice, I guess. >sigh<