Although I haven't tried deploying such an environment yet, I believe Azure DevTest Labs would allow deploying even complex infrastructures using Azure Resource Manager templates. As mentioned in the docs, these environments can contain any Azure resources that Resource Manager templates can create.
I tried forking the DevTest Labs public GitHub repository to quickly check and reproduce the issue. But I was able to add my repo as a template repository and browse through the templates on the Azure portal under {MyDevTestLab} > Virtual machine bases > Public environments. (Did you try this too?)
Next, ensure that the PAT created has adequate access via appropriate "read" or "repo" scopes. If that works well, then verify your Azure Resource Manager template folder paths. Note that it is relative to your git clone URI. For example, I configured /Environments
as the path for my templates.
Please check these and let me know what you see so I can troubleshoot the issue further.