Pretty sure that currently the Shopify GraphQL Admin API does not provide direct support for modifying notification email templates.
There may be something with the REST API that could be used but as that is legacy as of October 1, 2024, Shopify states:
All apps and integrations should be built with the GraphQL Admin API.
Currently I think the only suitable approach here would be to have the merchant provide access to their notification template code, you make the necessary modifications, and then save it and test it. Unfortunately that is obviously not an ideal approach but until there is a way to read and write the content via the GraphQL Admin API that’s the only one that is appropriate at the moment.
@Liam-Shopify any sort of extra information you could add here would be helpful. Specifically, whether or not there may be anything on the roadmap to enable such read and write down the road.