Sync "Check Website" workflow's trigger order with the template

No functional change, and neither is necessarily superior, but this is how it is in the template, and so it must be here
as well.

Author: per1234

.github/workflows/check-mkdocs-task.yml

@@ -1,7 +1,7 @@
 name: Check Website
 
 on:
-  pull_request:
+  push:
     paths:
       - ".github/workflows/check-mkdocs-task.ya?ml"
       - "Taskfile.ya?ml"
@@ -11,7 +11,7 @@ on:
       - "docs/**"
       - "docsgen/**"
       - "**.go"
-  push:
+  pull_request:
     paths:
       - ".github/workflows/check-mkdocs-task.ya?ml"
       - "Taskfile.ya?ml"