OK, I don't know how to make this issue be "solved", but here's the fix:
The problem was that I was following a tutorial by Acquia on YouTube that was like a year old. It was at some point making us install this:
composer require drush/drush:^10.1 --no-update
Fix: I reinstalled drush like this:
ddev composer require drush/drush -W
And then I was able to install admin_toolbar without a glitch!