Media Library Edit
This module adds an "Edit" button to the Media Library widget, allowing users to directly access and edit media items. It can open the edit form in a new tab or within a modal window for a better editing experience.
A tiny module to add a missing "Edit" button to the Media Library widget that routes to the Media entity edit form.
Once the module is enabled, click on the Manage Form settings gear for the relevant Media reference field using the Media LIbrary widget and enable the "Show edit" option.
Applies via third-party widget settings and the widget alter hook.
The 1.x branch opens a new browser window/tab with the media form. This is a simpler approach but has content UX limitations.
The 3.x branch opens the form in a modal, which is nicer for editors in most cases. See https://www.drupal.org/project/media_library_edit/issues/3034205 for info and potential limitations. This branch has replaced the 2.x branch, adding support for Drupal 10 and semantic versioning. The 2.x branch is available for Drupal 8 and 9.1 or below, but not supported.
If you'd rather patch core for this functionality, follow issue https://www.drupal.org/project/drupal/issues/2985168 . When merged to core, this module will be obsoleted.