WP treats plugins as content, literally in the same top level `wp-content` directory as uploaded images. This makes CI/CD among other things, a nightmare. But EmDash plugins are just TS modules, which has got to make things easier even if plugin configuration does end up in the db somewhere.
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.
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<
This just sounds like deploying web software. You always have static assets that need to be deployed, the code/binary itself, and database migrations.
The insane part is the search-and-replace on the database backup to find hard-coded URLs referencing the environment's hostname. That's ridiculous. It speaks to the lack of serious operational experience that went into building the software.
I moved away from Wordpress altogether earlier this year because I got tired of babysitting MySQL.