CiviCRM itself does not have user authentication. CiviCRM runs within a CMS: Wordpress, Drupal, Joomla or Backdrop. So IMO the question should be: does the CMS you will be using conform to the SAML 2.0 standard?
In my experience if 'localhost' (or your host) was refusing to connect on default port with all credentials/permissions definitely correct, specifying 'localhost:3306' will work (even though you shouldn't have to specify the :3306, and I think it tells you as much).
I will also note that this is something I have only experienced recently, and with this ...
One option to look at that will work for Wordpress to Wordpress and Wordpress to Drupal and Drupal to Drupal is using SimpleSAMLphp and an appropriate plugin.
The Drupal SimpleSAMLphp module https://www.drupal.org/project/drupalauth4ssp provides hooks which you can use to populate data from CiviCRM if you want to share this between the sites. (Note - you ...
Civi uses the CMS for authentication so the question is about configuring Drupal 7 (in your case) with Google SAML IDP.
I've not tried it, but a bit of googling shows a few links that look promising:
Drupal SAML Authentication module
Set up your own custom SAML application
CRM_Contact_BAO_Contact_Utils::generateChecksum($contactId) is the function used to generate checksums.
Ideally your extension would call this via a corresponding API method, but I don't think one exists yet?
There's corresponding code (see validChecksum etc below that) which is used in some CiviCRM pages to identify a request with a checksum parameter.