[CI] Fix update-website.yml (#25794)

Author: sbc100

.github/workflows/update-website.yml

@@ -1,6 +1,7 @@
 name: Update website
 
 on:
+  workflow_dispatch:
   push:
     branches: [ main ]
 
@@ -21,7 +22,7 @@ jobs:
         with:
           repository: kripken/emscripten-site
           ref: gh-pages
-          path: ../emscripten-site
+          path: site/emscripten-site
       - name: pip install
         run: |
           which python3

tools/maint/update_docs.py

@@ -24,7 +24,7 @@ def main(args):
   if args:
     site_out = args[0]
   else:
-    site_out = os.path.join(os.path.dirname(root_dir), 'emscripten-site')
+    site_out = os.path.join(root_dir, 'site', 'emscripten-site')
 
   assert os.path.isdir(site_out)
   print(f'Updating docs in: {site_out}')