This GitHub Action build html documentation by Sphinx, and push to branch gh-pages.

Select gh-pages branch as GitHub Pages source at repository settings.

Don't use this GitHub Action at branch gh-pages.

Setup workflow at branch master or docs may be a good idea.

example-sphinx.yml

on: [push]

jobs:
  build:
    name: Push Sphinx Pages
    runs-on: ubuntu-latest
    steps:
    - uses: seanzhengw/sphinx-pages@master
      with:
        github_token: ${{ secrets.GITHUB_TOKEN }}
        create_readme: true

There is a repo mydoc, it is Sphinx documentation source.

put example-sphinx.yml into mydoc/.github/workflows/

There are two branchs in repo myproject, branch master and branch docs.

The program source at branch master.

The Sphinx documentation source at branch docs.

To build GitHub Pages from branch docs, put example-sphinx.yml to branch docs only at myproject/.github/workflows/.

See https://seanzhengw.github.io/sphinx-pages, it from branch example.