All CLA requirements met.

Thanks a lot @pfitzseb !

Once this is merged and shipping, do we remove these parts from the Julia extension? Or is it best practice to still ship things in our extension in addition to having it in the core VS Code?

It would be best if you remove the duplication (grammar, language definition, language configuration) and instead depend on the basic extension.
You can always temporarily adding them back,e.g. if needed for an urgent fix when you don't want to wait for the next VSCode stable.

What's going on with the conversion code? Is this something I can/should fix upstream?

We had a bug in our grammar updater related to unicode. I pushed a fix 5cfa6b7 (microsoft/vscode-grammar-updater@3c5e198)

Thanks a lot for all your work @pfitzseb !

I added a Julia sample code that we use to run tests against. Feel free to have it cover more Julia syntax.
We use it to understand the changes after a grammar or theme update. We compare the tokens generated can colors assigned with the last known result.
It's perfectly fine to update the expected test results after a grammar update if we think the changes are making sense,

FYI @alexr00