Greetings! Finally get back to this. So, to hop in:
1) The credential being made is "Bitbucket personal access token".
2) The token I am trying to use is to add our Bitbucket Server instance to the System Configuration.
3) Yes, I see my token sitting in the credentials.xml file. I will say, however, there are multiple Bitbucket tokens in the XML file and even these don't appear in the dropdown. The type is as stated in your question.
4) Scope for mine is SYSTEM.
5) Errors seen include:

but the one that is seen a lot when attempting this is:

Hi Edwin thanks for the report.
To clarify the issue I need more information:
The list filters out any credentials not matching the "Bitbucket personal access token" type when specifying the access token, which is why some credentials do not appear in that list.
Thanks,
Martin