core.getInput (and maybe other things) doesn't work in another action

Please let me know if I'm just doing things wrong, but when actions/github-script is used within another action, things like core.getInput('some_input) don't return anything.

I have a test here to demonstrate: https://github.com/daleyjem/test-github-script/pull/1

Workflow File

name: Test
on:
  pull_request:
    types: [opened, synchronize]

jobs:
  test:
    name: test
    runs-on: ubuntu-latest
    steps:
      - name: Checkout
        uses: actions/checkout@v2
      - name: Test input
        uses: ./.github/actions/test-input

Action File

name: Test Input
description: Test input
inputs:
  my_input: 
    description: My input
    required: false
    default: 'foobar'

runs:
  using: 'composite'
  steps:
    - name: Log input val
      uses: actions/github-script@v6
      with:
        script: |
          console.log('my_input =', core.getInput('my_input'))
    - name: Log it the other way
      run: |
        echo ${{ inputs.my_input }}
      shell: bash

Start with the linked reproduction, especially its workflow file and .github/actions/test-input composite action, then compare core.getInput('my_input') with ${{ inputs.my_input }}. Done means determining whether composite-action inputs should be available to the nested actions/github-script step and adding a regression test or documenting the supported behavior.