Updating Drupal with Composer
The guide Updating Drupal core via Composer does a very good job of describing the various steps. The notes below are from practice.
Upgrading from 8.9.1 to 8.9.11:
# Look-up updates.
composer outdated drupal/*
# Look-up prerequisites for updating core to the target version.
composer prohibits drupal/core-recommended:8.9.11
# Update core and dependencies.
composer update drupal/core 'drupal/core-*' --with-all-dependencies
# Run database updates and export any resulting config changes.
drush updatedb
drush cache:rebuild
drush config:export --diff
The same steps apply to Drupal 9, 10, and 11. Only the version numbers change.