Run VS Code tests on CI

This is actually much faster than I expected; it takes about 13 seconds
to download VS Code and run the unit tests. This means the VS Code tests
are still significantly faster than the Rust ones.

If this ends up being unreliable we can always remove it later or move
it to a separate optional job.

We also need to ignore the `.vscode-test` directory when running
`prettier` or it will get upset about some temporary JSON files VS Code
creates.

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