Upgrading from Drupal 9 to Drupal 10

1. Install Upgrade Status[https://www.drupal.org/project/upgrade_status] module to check issues contrib and custom modules compatibility. 

2. Remove Upgrade Status when all checks are green and ready to go. Uninstall Upgrade status and remove it from Composer.

 
composer remove drupal/upgrade_status 

3. Temporarily add write access to protected files and directories
chmod 777 sites/default chmod 666 sites/default/*settings.php chmod 666 sites/default/*services.yml 

4. Upgrade Drupal Core and modules
composer require 'drupal/core-recommended:^10' 'drupal/core-composer-scaffold:^10' 'drupal/core-project-message:^10' --no-update 

5. If Drush is present, upgrade to 12
composer require 'drush/drush:^12' --no-update 

6. If core-dev is present, this might be required
composer require 'drupal/core-dev:^10' --dev --no-update 

7. Do a dry run
composer update --dry-run 

8. If no errors, upgrade
composer update 

9. Verify again if no errors on update in step before with install
composer install 

10. Update Database and Export config
drush updatedb -y && drush cex -y 

11 Restore read only acces
chmod 755 sites/default chmod 644 sites/default/*settings.php chmod 644 sites/default/*services.yml 

Links -- https://www.drupal.org/docs/upgrading-drupal/upgrading-from-drupal-8-or-later/how-to-upgrade-from-drupal-9-to-drupal-10