PYTHON-5047 Fix dry run logic in releases again (#2092)

(cherry picked from commit b4e32a1)

Author: blink1073

.github/workflows/release-python.yml

@@ -23,7 +23,7 @@ env:
   SILK_ASSET_GROUP: mongodb-python-driver
   EVERGREEN_PROJECT: mongo-python-driver
   # Constant
-  DRY_RUN: ${{ inputs.dry_run == 'true' }}
+  DRY_RUN: ${{ github.event_name == 'workflow_dispatch' && inputs.dry_run || 'true' }}
   FOLLOWING_VERSION: ${{ inputs.following_version || '' }}
   VERSION: ${{ inputs.version || '10.10.10.10' }}