Error: Cannot find module 'cypress'

We just attempted to update to v2 and are now getting the following error when running Cypress. Here is our action config:

jobs:
  end-to-end-tests:
    name: End-to-End tests (web)
    runs-on: ubuntu-latest
    if: github.event.pull_request.draft == false
    steps:
      ## Start Shared Setup
      - name: checkout gather
        uses: actions/checkout@v2

      - name: setup node
        uses: actions/setup-node@v2-beta
        with:
          node-version: 12.18.3

      - uses: bahmutov/npm-install@HEAD
      ## End Shared Setup

      - name: cypress in chrome
        uses: cypress-io/github-action@v2
        with:
          browser: chrome
          headless: true
      - name: upload failure screenshots
        uses: actions/upload-artifact@v2
        if: failure()
        with:
          name: cypress-screenshots
          path: cypress/screenshots
      - name: upload failure videos
        uses: actions/upload-artifact@v2
        if: failure()
        with:
          name: cypress-videos
          path: cypress/videos

and for reference, the previous config:

jobs:
  end-to-end-tests:
    name: End-to-End tests (web)
    runs-on: ubuntu-latest
    if: github.event.pull_request.draft == false
    steps:
      ## Start Shared Setup
      - name: checkout gather
        uses: actions/checkout@v2

      - name: setup node
        uses: actions/setup-node@v2-beta
        with:
          node-version: 12.18.3

      - uses: bahmutov/npm-install@HEAD
      ## End Shared Setup

      - name: cypress in chrome
        uses: cypress-io/github-action@v1
        with:
          browser: chrome
          headless: true
      - name: upload failure screenshots
        uses: actions/upload-artifact@v1
        if: failure()
        with:
          name: cypress-screenshots
          path: cypress/screenshots
      - name: upload failure videos
        uses: actions/upload-artifact@v1
        if: failure()
        with:
          name: cypress-videos
          path: cypress/videos

After running we get the following output:

##[debug]Cypress versions in the cache folder /home/runner/.cache/Cypress
/opt/hostedtoolcache/node/12.18.3/x64/bin/npx cypress cache list
┌─────────┬──────────────┐

│ version │ last used    │
├─────────┼──────────────┤
│ 6.0.0   │ a minute ago │
└─────────┴──────────────┘
##[debug]no need to verify Cypress binary or save caches
##[debug]No start command found
##[debug]Running Cypress tests using NPM module API
##[debug]requiring cypress dependency, cwd is /home/runner/work/calm/calm
##[debug]working directory /home/runner/work/calm/calm
##[debug]Cannot find module 'cypress'
##[debug]Require stack:
##[debug]- /home/runner/work/_actions/cypress-io/github-action/v2/dist/index.js
##[debug]Error: Cannot find module 'cypress'
##[debug]Require stack:
##[debug]- /home/runner/work/_actions/cypress-io/github-action/v2/dist/index.js
##[debug]    at Function.Module._resolveFilename (internal/modules/cjs/loader.js:797:15)
##[debug]    at Function.resolve (internal/modules/cjs/helpers.js:80:19)
##[debug]    at runTests (/home/runner/work/_actions/cypress-io/github-action/v2/dist/index.js:9094:13)
##[debug]    at processTicksAndRejections (internal/process/task_queues.js:93:5)
Error: Cannot find module 'cypress'
Require stack:
- /home/runner/work/_actions/cypress-io/github-action/v2/dist/index.js
##[debug]Node Action run completed with exit code 1
##[debug]CI='1'
##[debug]CYPRESS_CACHE_FOLDER='/home/runner/.cache/Cypress'
##[debug]CYPRESS_CACHE_FOLDER='/home/runner/.cache/Cypress'
##[debug]CYPRESS_CACHE_FOLDER='/home/runner/.cache/Cypress'
##[debug]TERM='xterm'
##[debug]Finishing: cypress in chrome

The above is with the following added to the action:

  ACTIONS_RUNNER_DEBUG: true
  ACTIONS_STEP_DEBUG: true