Have commits made by pull request skip branch protection rules

I have a complex action that builds to some environments over several steps. As part of this process I want it to push a single file generated by this build process to my integration branch (which is the current branch this action is running under). I also have a few branch protection rules on my integration branch to prevent merges from happening without checks / reviews taking place. However, with the branch protection rule in place, the commit fails with the following output:

Already on 'integration'
M	.github/deltas/stable_md5.txt
Your branch is up to date with 'origin/integration'.
From https://github.com/[PRIVATE_REPOSITORY]
 * branch            integration -> FETCH_HEAD
Already up to date.
[integration 709ab96] update to stable delta hash file
 1 file changed, 2 insertions(+), 2 deletions(-)
remote: error: GH006: Protected branch update failed for refs/heads/integration.        
remote: error: Required status check "pmd" is expected. At least 1 approving review is required by reviewers with write access.        
To https://github.com/[PRIVATE_REPOSITORY]
 ! [remote rejected] HEAD -> integration (protected branch hook declined)
error: failed to push some refs to 'https://github.com/[PRIVATE_REPOSITORY]'

I have the following relevant step:

- name: Commit Delta File to Branch
  run: |
    git fetch
    git checkout integration
    git pull origin integration
    git config --global user.email "bslaght@salesforce.com"
    git config --global user.name "@bslaghtSFDC"
    git add .github/deltas/${TARGET_BRANCH}_md5.txt
    git commit -m "update to ${TARGET_BRANCH} delta hash file"
    git push origin HEAD:integration
  shell: bash

How can I get this protection rule to not apply to workflows? I am an admin to the repository in question and the branch protection rule does not apply to admins so my assumption was that this workflow would be able to ignore the protection rule. Thanks in advance.