Drupal 9 Supports PHP 7.4 but the recommended PHP version is 8.0 or higher recommended. Check below documentation for a clear idea.
Drupal - PHP requirements
You can disableupdate notificationsby disabling theUpdate Managermodule, which is responsible for checking and informing about available updates.
Navigate to Extend -> Search for "Update Manager" and disable the module.
This is not recommended but you can keep this module enabled in your development environment and know when a security updates are released.
Drupal 10 is around the corner and it only supports PHP 8.1 and above. You should better migrate to a different hosting provider as soon as possible.