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How can I ask for a stable version of the module?

You can't install a stable version of Taxonomy Menu module for Drupal 9 at the moment because no such version exists.
If you look at the project page, you see the latest version is 3.4 which is marked Requires Drupal: 8.x.



So, if you want to use a stable version, you have to stay with Drupal 8 for now.
To use the dev version on Drupal 9, you can do this in composer.json:
    &quot;drupal/taxonomy_menu&quot;: &quot;3.x-dev&quot;,

Normally you should not need to authenticate to git.  It's probably a proxy issue; you might find some hints in this discussion.