My view is to be able to programmatically trigger a build without having to add a commit to the github repository. Answering your questions:
What do you mean by ‘webhook triggering third party snap build’?
A script or application hosted on my own infrastructure triggers the BSI build to initiate.
Where the snap code would be hosted?
GitHub
Where would snapcraft.yaml live (if upstreams are not willing to maintain snap package)?
GitHub