Update documentation workflow triggers based on SQuaRE template

Use the triggers from this template:

https://github.com/lsst/templates/blob/main/project_templates/square_pypi_package/example/.github/workflows/ci.yaml

.github/workflows/doc.yaml

@@ -1,12 +1,21 @@
 name: Build and upload documentation
 
-on:
+"on":
+  merge_group: {}
+  pull_request: {}
   push:
-    branches:
-      - main
-    tags:
-      - "*"
-  pull_request:
+    branches-ignore:
+      # These should always correspond to pull requests, so ignore them for
+      # the push trigger and let them be triggered by the pull_request
+      # trigger, avoiding running the workflow twice.  This is a minor
+      # optimization so there's no need to ensure this is comprehensive.
+      - "dependabot/**"
+      - "gh-readonly-queue/**"
+      - "renovate/**"
+      - "tickets/**"
+      - "u/**"
+  release:
+    types: [published]
 
 jobs:
   build_sphinx_docs:
@@ -49,4 +58,7 @@ jobs:
           dir: doc/_build/html
           username: ${{ secrets.LTD_USERNAME }}
           password: ${{ secrets.LTD_PASSWORD }}
-        if: github.event_name != 'pull_request'
+        if: >
+          github.event_name != 'merge_group'
+          && (github.event_name != 'pull_request'
+              || startsWith(github.head_ref, 'tickets/'))