I'm getting closer with this but still running into some issues. I've managed to create a remote repo and connect that to my local repo outside the context of DM. DM recognizes the local repo just fine and I can use it for local commits. But when I try to push I get this:
In bash, I can push that same commit with no issues:
If I try to pull inside DM I get a similar error:
Note that the height of the error response is cutting off the full message.
I must be missing something related to how DM can read/access my public key but not sure where to look for more clues. This is the dialog I get from DM overlaid on my bash shell when I click the Remote button. Perhaps using ssh vs https?

Well, that's an error coming from Git. Make sure you can push with that account using your normal git client or command line. Pretty sure that also won't work - looks like you have read-only access to Git in this case.
FWIW, you can mix and match Git clients. Most places in the UI let you Open in Terminal (Tab, Context Menu, Tools etc.) and from there you can use command line with Git as needed as well.
+++ Rick ---
On second thought:
Your Git Repo is accessed through the permissions that are set up in the Git command in Windows. The only thing I can think of is that you're using Git through Bash which is not using the raw Windows environment, but Windows Subsystem for Linux or the Bash Shell (also some Linux shell). IOW, you're not using the Windows installed version of Git which is likely configured separately and which is what any desktop client will be using (ie. Documentation Monster, Markdown Monster etc.).
FWIW, you don't need Bash to access Git - you can use Command or PowerShell and that's how at the very least you can debug and see if you get the same behavior and you can debug from there. Or use a visual Git Client. Or if you use WSL I think there's a shared version of Git that uses the Windows install of it.
FWIW, you can mix and match Git clients. Most places in the UI let you Open in Terminal (Tab, Context Menu, Tools etc.) and from there you can use command line with Git as needed as well.
IAC make sure you use the Windows version of Git and that that version of Git has the required credentials set up for your Repo (ie. Windows Credential Store most likely).
FWIW setting that up is likely going to be easier via some of the full Git Client like GitHub Desktop, GitKraken, SourceTree, SmartGit etc.
Thanks.
Yeah, I know I can use other shells. I'm using the bash shell that comes with the git Windows distro. Been doin git stuff this way for years. I run Pageant at startup and add my preferred identity. In bash, I get the PID and add my identity there. My shell is up and running all the time so it's a one-time thing.
What I was trying to show in my screenshots is that I can push and pull for this repo in bash; the failure is happening with the git integration in DM. But I think you're on to something as far as the available identities loaded in that context. If DM is effectively using ssh in the same context as PS then I have another clue.

I was able to start the ssh-agent service via PS and add my identity.
But DM is still not happy.
You said I can invoke a shell directly from DM? That option isn't jumping out and biting me...
FWIW I do use a GUI git client. Years ago when I first started with git I installed Sourcetree but I haven't used that in ages. The shell works fine for me. I am successfully using some of the integrated git plugins for VS Code but otherwise no dedicated GUI client.
Found the Open Folder in Terminal option. Will see what I can see.
Running git commands from a terminal invoked from inside DM gives the same fatal results. Personally I can live with pushing to the remote from my standard bash shell but once I get others using this, particularly the non-engineer, I'll have to figure out why it's not finding what it needs.