What TextMate scope is used for "normal code/text" in VS Code?

I'm trying to create a TextMate grammar for a language that can have interpolated code sections in any string. So everything between <% and %> inside any string is "normal" code, which can have strings again. I want to use the grammar for a VS Code extension.

My multi-line strings are enclosed by <<->>.

I think it is not possible to handle this case for arbitrary depth, so I would be happy to get it to work for simple cases with nesting up to some depth.

What would the patterns look like for the following code?

<<
This is some string
<%This is normal code
  <<
  This is more <%Normal code%>string <%More code%>
  >>%>
And of course more string
>>

I tried to use the following myLanguage.tmGrammar.yaml:

name: myLanguage
scopeName: source.myLanguage

patterns:
  - begin: <<
    end: ">>"
    name: string.quoted.double
    patterns:
        - begin: <%
          end: "%>"
          include: source.myLanguage

  - begin: <%
    end: "%>"
    name: variable  # <--- What is the name for "default code"?
    patterns:
        - begin: <<
          end: ">>"
          include: source.myLanguage

It mostly works, but I need to use "normal" code instead of keyword highlighting.

I followed the advice and looked at the TestMate grammar of JavaScript and adapted the backtick strings for my language.

Here is the resulting grammar:

name: myLanguage
scopeName: source.myLanguage

patterns:
  - include: '#strings'

repository:
  strings:
    begin: '<<'
    end: '>>'
    name: string.quoted.double
    patterns:
      - include: '#interpolation'
  interpolation:
    begin: '<%'
    end: '%>'
    contentName: source.myLanguage
    name: meta.embedded
    patterns:
      - include: $self

The normal code part is highlighted as normal text. Expanding on this I was able to do more highlighting within the "normal code" sections inside <%-&>-blocks.