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Yep. There's a plugin API, https://docs.logseq.com/#/page/Plugins, used by 180+ plugins. Logseq can also be scripted from the commandline in node.js with https://github.com/logseq/nbb-logseq#projects-using-nbb-logs.... There are examples for creating a github action, a CLI or creating custom web apps

You can write simplified queries in its own DSL, more complex queries in Datalog and plugins in ClojureScript, JavaScript or Typescript.

(The plugin API still feels a little quirky, though)

Yes, you can write plugins in typescript to create very powerful integrations like VSCode.

I wrote a plugin for openai gpt3 https://github.com/briansunter/logseq-plugin-gpt3-openai

It exposes limited scripting in Clojure if you don't to write a plugin in JavaScript. I wouldn't say it's fully programmable but somewhere in-between.

There is a plugin system, so I'd expect you to be able to go crazy with it.