The services user.private_tempstore and user.shared_tempstore are deprecated in favour of tempstore.private and tempstore.shared. Code that uses the User module services should be updated to use the new services from core.
Any typehints or documentation pointing to the following classes should be updated accordingly:
Drupal\user\PrivateTempStore -> Drupal\Core\TempStore\PrivateTempStore
Drupal\user\PrivateTempStoreFactory -> Drupal\Core\TempStore\PrivateTempStoreFactory
Drupal\user\SharedTempStore -> Drupal\Core\TempStore\SharedTempStore
Drupal\user\SharedTempStoreFactory -> Drupal\Core\TempStore\SharedTempStoreFactory
Drupal\user\TempStoreException -> Drupal\Core\TempStore\TempStoreException
In order to minimise disruption and preserve BC Drupal\user\TempStoreException is aliased to Drupal\Core\TempStore\TempStoreException if you use the deprecated services no code change is required.
If your site has customised the user.tempstore.expire container parameter this should be changed to tempstore.expire.