Does this mean I cannot use Bitbucket, Opsgenie etc. REST APIs in a Forge JIRA Custom UI app because of the lack of the Atlassian Oauth support?
Not exactly. To my knowledge, Opsgenie does not have OAuth 2 so could not be reached using the external auth module. But that doesn’t rule out API tokens, which both Opsgenie and Bitbucket provide (Bitbucket calls them app tokens). Atlassian is aware this isn’t a great experience and does intend to better support cross-product apps; however, that intention is not really a plan yet so I don’t see any on the near-term horizon that will solve this problem as a Forge feature. In the meantime, your app would have to obtain API tokens.
I realize the cross-product topic is confusing so all questions are welcome. I would ask that folks create new threads to ask those questions. This one is specific to OAuth-based external auth so I’m locking it until/if Atlassian solves for the messaging that @zsims mentioned.