Note - the user did not say he/she had uninstalled the module, but theat he/she had deleted the instance of the Module from the Host/Module Definitions page.

This module can be recoved (to a degree) by adding it back to the page from the control panel (it is an Extensions module, with custom settings).  At this time the Extensions module does not expose those settings so you will get a duplicate of the version on Host/Extensions.

The Module Definitions module is now a customised version of the Extensions module - customised by a Module Setting.  There is currently no Settings UI page however to manage that.

I probably overstepped by saying it wasn't a bug - there is a bug in that once deleted it is not trivial to replace the module - due to the lack of UI configuration.

It is however important to realise however that the user has experienced NO loss in functionality as the Module he deleted was a reduced functionality version of the Extensions module - you can do everything through the Extensions module - it also contains the ability to manage other extensions - the missing setting enables ONLY the module definitions part of the Extensions module.

Anyway in order to "fix" this will require some database manipulation - to add the missing Module Setting.  Find the module id by selecting the Manage Settings action from the Action menu, and in the Module Settings table add the following Module Settings

ModuleID - value of mid querystring parameter
SettingName - Extensions_Mode
SettingValue - Module

You can create a Gemini issue for this BUT it is likely the "separate" Module Definitions page will be dropped in the UI overhaul in favour of the Extensions page anyway.