Rewrite integration tests to use Vite Browser Mode

[a-type]

Fake DOM environment junk keeps biting me. Need to ditch undici, fake-indexeddb, et al.

Main issue here is running the server for the tests. But it might actually be a good meta-test to share 1 server for all of them? So tests run in browser tabs and communicate to one server process. The server can expose custom HTTP endpoints for any extra functionality like manipulating the filesystem or fetching metadata.

Still this will be a pain.