Persistant "Component class 'benf\neo\Field' belongs to an uninstalled plugin (Neo)" error

Description

This ticket is related to this Neo ticket, but I'm posting it here also as it may be a more general related Craft CMS issue.

I have a project that required multiples branches, and multiple databases (as a few settings where stored in DB only, not in project config).
After merging from one branch to another, I got this error:
Component class 'benf\neo\Field' belongs to an uninstalled plugin (Neo).

It's not the first time I got it and can easily fix it like this:
composer require spicyweb/craft-neo

When it's not enough:

1. I try again with composer remove spicyweb/craft-neo before the other one
2. I run ./craft plugin/enable neo

Or alternatively:

1. Uninstall plugin from /admin/settings/plugins
2. Install plugin from /admin/settings/plugins

Unfortunately, I still got the same error that the plugin is missing.
Even after running:

./craft project-config/rebuild
./craft project-config/apply

In /admin/settings/fields all my Neo fields are still showing benf\neo\Field in red color text.

Any idea how to fix this?

Other information

• Neo version: 2.12.1
• Craft version: 3.7.27.1
• Multi-site: yes, but without propagation
• Is eager-loading used? No

Start by reproducing the missing-plugin state using the reported Craft and Neo versions, then compare the project-config rebuild/apply commands with the plugin enable and install flows. Check the admin Settings > Fields view to trace why Neo fields still appear as benf\neo\Field and confirm that the uninstalled-plugin error and red field labels are gone.