That's an interesting use case! We have no plans to build an integration like this, mainly given maintenance overhead on our side and not being dbt experts ourselves. So this could be a great community maintained integration.
It seems like majority of the work is done in this repo:
https://github.com/louisguitton/dbt-metadata-utils
You'd have to send the data on the backend to Typesense’s API instead of Algolia and on the frontend use the typesense-instantsearch-adapter