Phase 1: generate database types and type the Supabase clients

Types are generated from the live database's API schema by
scripts/gen-types.mjs (npm run gen:types), in the same shape as
supabase gen types, so no Supabase CLI login is needed.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

package.json

@@ -9,7 +9,8 @@
     "lint": "eslint",
     "test": "vitest run",
     "test:watch": "vitest",
-    "check:rls": "node --env-file=.env.local scripts/check-rls.mjs"
+    "check:rls": "node --env-file=.env.local scripts/check-rls.mjs",
+    "gen:types": "node --env-file=.env.local scripts/gen-types.mjs"
   },
   "dependencies": {
     "@supabase/ssr": "^0.12.7",