monaco-editor version: 0.19.3
Browser: Chrome 79
OS: macOS
Playground code that reproduces the issue:

According to the Monarch docs:

If it starts with a ^ character, the expression only matches at the start of a source line.

I have tried both specifying a regex literal /^!/ as well as a string "^!", but neither works.

You can reproduce the issue on the special Monarch playground at https://microsoft.github.io/monaco-editor/monarch.html. In the Language syntax definition, specify:

return {
  // The main tokenizer for our languages
  tokenizer: {
    root: [
      [/^\!/, {token: 'delimiter.curly', next: 'jsonInBang', nextEmbedded: 'json'}],
    ],
    jsonInBang: [
      [/^\!/, {token: 'delimiter.curly', next: '@pop', nextEmbedded: '@pop'}],
    ],
  },
};

And then in the Language editor, specify:

!
  {
    "foo": "bar",
    "baz": 42,
    "quux": [
      {
        "foo": "bar!",
      }
    ],
    "quux2": [
      {
        "foo": "bar",
      }
    ]
  }
!

If you look carefully, the JSON inside the ! starts out being highlighted correctly, but after the ! in the string literal "bar!", it stops working. It appears the /^\!/ has matched it even though it is not the start of a source code line, which is not what the docs claim should happen.