I am afraid it isnot possible to create an extension that adds pipeline template to template selector. I didnot find there is a rest api for creating build templates.
And when calling build templates api to get the existing build templates. The customized template is pointed to an existing build definition in the Azure organization. Check the highlighted in below screenshot.
That is to say the build definition must exist first in the external clients's organization. If the build definition already exists, there would be no need to distribute your azure devops yaml pipeline template.
Since yaml pipeline is defined in the YAML file in the repo, it would be much easier to distribute your yaml file to external clients.
And you can let them to create a pipeline by using the distributed yaml file. If they want to create a template from it. They can save the pipeline as template from their side.
Go to Builds under Pipelines--> select the pipeline--> Click the three dots and choose save as template
(Noted: Custom Build Template is disabled in the new feature experience. You have to disable Multi-stage pipelines from the Preview Features)
