test: run supabase locally during test (#35947)

Alter the docs test script so it spins up Supabase locally. Will allow
for end-to-end tests against the local DB.

Also small alteration to one of the test files to silence an annoying
(but intended) error.

.github/workflows/docs-tests.yml

@@ -25,6 +25,7 @@ jobs:
             apps/docs
             examples
             packages
+            supabase
 
       - uses: pnpm/action-setup@v4
         name: Install pnpm