We currently use Google SSO for our JIRA system. The Aha! integration however requires a username/password user account & not an SSO user.
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Atlassian has added a capability to Jira Cloud specifically to address this issue. It is called API tokens: https://confluence.atlassian.com/cloud/api-tokens-938839638.html. You can use API tokens now with Aha!.
This feature does not appear to be available yet for Jira Server.