How can I add a commit to a dependabot PR and run all checks?

Question

I'm trying to bump the version on a repository when creating dependabot PR's. But ran into a few issues. I'm using the following workflow (summarized):

permissions:
  contents: write

on:
  pull_request:
    types: [opened, synchronize]
    branches:
      - main

jobs:
  build:
    runs-on: ubuntu-latest
    if: github.actor == 'dependabot[bot]'
    steps:
      - uses: actions/checkout@v4
        with:
          ref: ${{ github.event.pull_request.head.ref }}
      - name: bump version
        run: |
          ...
      - name: commit
        run: |
          git config --global user.name "dependabot[bot]"
          git config --global user.email "dependabot[bot]@users.noreply.github.com"
          git commit -a -m "version update"
          git push

The issues which I ran into is that the new commit won't have any github actions ran on them. This means checks are not displayed as completed in the PR. How can I solve this issue?