chore: Fix broken pypi publish action

According to [this GitHub issue][1], the `pypa/gh-action-pypi-publish`
action cannot be used in nested actions. This commit inlines the usage
of this action into the top-level workflows instead.

[1]: pypa/gh-action-pypi-publish#299

Author: keelerm84

.github/actions/publish/action.yml

@@ -35,10 +35,11 @@ jobs:
       - uses: ./.github/actions/build
         id: build
 
-      - uses: ./.github/actions/publish
+      - name: Publish package distributions to PyPI
+        if: ${{ inputs.dry_run == false }}
+        uses: pypa/gh-action-pypi-publish@release/v1
         with:
-          token: ${{env.PYPI_AUTH_TOKEN}}
-          dry_run: ${{ inputs.dry_run }}
+          password: ${{env.PYPI_AUTH_TOKEN}}
 
   release-provenance:
     needs: [ 'build-publish' ]

.github/workflows/manual-publish.yml

@@ -47,11 +47,11 @@ jobs:
       - uses: ./.github/actions/build-docs
         if: ${{ steps.release.outputs.releases_created == 'true' }}
 
-      - uses: ./.github/actions/publish
+      - name: Publish package distributions to PyPI
         if: ${{ steps.release.outputs.releases_created == 'true' }}
+        uses: pypa/gh-action-pypi-publish@release/v1
         with:
-          token: ${{env.PYPI_AUTH_TOKEN}}
-          dry_run: false
+          password: ${{env.PYPI_AUTH_TOKEN}}
 
   release-provenance:
     needs: [ 'release-package' ]