chore: Publish docs on push to main (#385)

## Description

Publish docs on push to main.

### Type of change

- [ ] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [ ] Breaking change (fix or feature that would cause existing
functionality to not work as expected)
- [ ] Documentation update (improves or adds clarity to existing
documentation)

### Checklist
- [x] I have performed a self-review of my code
- [x] I have commented my code, particularly in hard-to-understand areas
- [x] I have updated the documentation accordingly
- [x] My changes generate no new warnings

Author: jakmro

.github/workflows/publish_docs.yml

@@ -1,6 +1,12 @@
 name: Publish to GitHub Pages
 
 on:
+  push:
+    branches:
+      - main
+    paths:
+      - '.github/workflows/publish_docs.yml'
+      - 'docs/**'
   workflow_dispatch:
 jobs:
   publish: