UPDATE: I think this question was based on a fundamental misunderstanding. When creating the build pipeline definition, I would pick the saved service connection ("GitHub-iQmetrixService" in the screenshot), and then later Azure DevOps would continue to prompt for access to my personal account. This made me think that the build pipeline was linked to my personal account somehow, such that if my account is ever in the future gone or otherwise unable to access the repository, the build pipeline would stop working.
As far as I now understand, this is not the case. The build pipeline definition itself is in fact associated with the service connection, and the reason that Azure DevOps prompts for my personal login is because the integrated YAML editor is going to want to make commits back to the repo, and those commits need to happen "as me". When co-workers go to the pipeline editor, they too are prompted for their personal login.
I'm still a little bit nervous about this understanding, because I can't see anything in the UI that shows what service connection Azure DevOps is using primarily to process the build pipeline, nor can I see any way to change it should that ever be necessary.
When creating a new Build Pipeline, if I tell Azure DevOps that my repository is in GitHub, I am immediately redirected to GitHub to authorize access to my personal GitHub account (to which I have an ambient login). If I instead pick "Other Git", then the next step in the flow lets me say that the source is GitHub, at which point the screen says:
This authorization, set up by someone else in my organization, works just fine, and I can view all of the organization's repositories and set up a new pipeline. But then, if I close the window and try to re-open the pipeline editor, I am immediately redirected once again to the GitHub page to authorize access to my personal account. Editing the pipeline created based on the "GitHub-iQmetrixService" connection does not use the connection and instead wants to establish a new connection based on whatever individual accounts I have access to.
How can I edit the pipeline without creating a connection to the repository that is linked to my own personal account?