Logseq can expose an HTTP API: https://docs.logseq.com/#/page/local%20http%20server

This is less ideal than a library due to the complexity of running it; setting it up on a server will probably be annoying. But it should give you a lot of the power Logseq has, it apparently being the same API as plugins get to use.

When Logseq is running locally, you can use its [local http server](https://docs.logseq.com/#/page/local%20http%20server) to do this. https://github.com/logseq/nbb-logseq is useful for automations and is already used to create github actions e.g. https://github.com/logseq/publish-spa. In the upcoming database version, nbb-logseq is able to read and write Logseq graphs completely independent of the app - https://github.com/logseq/docs/blob/feat/db/db-version.md#sc...

I don't know of any at the moment. That said I do want to add the ability to search pages and navigate links within the Logseq graph. This would have to be in the TUI as I don't want to maintain several plugins for various editors.