For browser, there is a webapp that can be selfhosted. See here https://github.com/logseq/logseq/blob/master/docs/docker-web-app-guide.md

I think you need chromium browsers due to the API they use, but it should work.

Yes, you could run it in LAN only. You could access it via VPN only.

Obviously this adds friction in addition to security, but if that’s fine with you, you can.

Thanks for the head’s up!