Can't install any version of the module with composer

Problem/Motivation

Can't install the module with composer: "Your requirements could not be resolved to an installable set of packages."

Steps to reproduce

On a virgin Drupal 10.0.9 install, run:

1. composer require 'drupal/mixitup_views:^1.0' (like stated in the module page, of course needs to be updated):

  Problem 1
    - drupal/mixitup_views[1.0.0, ..., 1.1.0] require composer/installers ^1.2 -> found composer/installers[v1.2.0, ..., v1.12.0] but it conflicts with your root composer.json require (^2.0).
    - drupal/mixitup_views[1.11.0, ..., 1.12.0] require drupal/core ^8 || ^9 -> found drupal/core[8.0.0, ..., 8.9.20, 9.0.0, ..., 9.5.9] but the package is fixed to 10.0.9 (lock file version) by a partial update and that version does not match. Make sure you list it as an argument for the update command.
    - Root composer.json requires drupal/mixitup_views ^1.0 -> satisfiable by drupal/mixitup_views[1.0.0, 1.1.0, 1.11.0, 1.12.0].

2. composer require drupal/mixitup_views:

  Problem 1
    - drupal/mixitup_views[1.0.0, ..., 1.1.0, 3.0.1, ..., 3.0.2] require composer/installers ^1.2 -> found composer/installers[v1.2.0, ..., v1.12.0] but it conflicts with your root composer.json require (^2.0).
    - drupal/mixitup_views[1.11.0, ..., 1.12.0, 2.0.0, ..., 2.2.0] require drupal/core ^8 || ^9 -> found drupal/core[8.0.0, ..., 8.9.20, 9.0.0, ..., 9.5.9] but the package is fixed to 10.0.9 (lock file version) by a partial update and that version does not match. Make sure you list it as an argument for the update command.
    - Root composer.json requires drupal/mixitup_views * -> satisfiable by drupal/mixitup_views[1.0.0, 1.1.0, 1.11.0, 1.12.0, 2.0.0, 2.1.0, 2.2.0, 3.0.1, 3.0.2].

3. composer require 'drupal/mixitup_views:^3.0':

  Problem 1
    - Root composer.json requires drupal/mixitup_views ^3.0 -> satisfiable by drupal/mixitup_views[3.0.1, 3.0.2].
    - drupal/mixitup_views[3.0.1, ..., 3.0.2] require composer/installers ^1.2 -> found composer/installers[v1.2.0, ..., v1.12.0] but it conflicts with your root composer.json require (^2.0).

4. & 5. composer require 'drupal/mixitup_views:3.0.x-dev@dev' or even with --with-all-dependencies (-W) option:

  Problem 1
    - drupal/mixitup_views dev-3.0.x requires composer/installers ^1.2 -> found composer/installers[v1.2.0, ..., v1.12.0] but it conflicts with your root composer.json require (^2.0).
    - drupal/mixitup_views 3.0.x-dev is an alias of drupal/mixitup_views dev-3.0.x and thus requires it to be installed too.
    - Root composer.json requires drupal/mixitup_views 3.0.x-dev@dev -> satisfiable by drupal/mixitup_views[3.0.x-dev (alias of dev-3.0.x)].

Proposed resolution

Remaining tasks