Migrate backend from Lovable Cloud to own Supabase (EDU project)

- Point .env + supabase/config.toml at EDU (qgmcpounpkgsjlwosjdi)
- Replace Lovable Google-OAuth shim with native supabase.auth.signInWithOAuth
- Remove src/integrations/lovable and @lovable.dev/cloud-auth-js dependency
- Drop .lovable metadata; gitignore supabase/.temp

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

bun.lock

@@ -6,7 +6,6 @@
       "name": "tanstack_start_ts",
       "dependencies": {
         "@hookform/resolvers": "^5.2.2",
-        "@lovable.dev/cloud-auth-js": "^1.1.2",
         "@radix-ui/react-accordion": "^1.2.12",
         "@radix-ui/react-alert-dialog": "^1.1.15",
         "@radix-ui/react-aspect-ratio": "^1.1.8",
@@ -232,8 +231,6 @@
 
     "@jridgewell/trace-mapping": ["@jridgewell/trace-mapping@0.3.31", "", { "dependencies": { "@jridgewell/resolve-uri": "^3.1.0", "@jridgewell/sourcemap-codec": "^1.4.14" } }, "sha512-zzNR+SdQSDJzc8joaeP8QQoCQr8NuYx2dIIytl1QeBEZHJ9uW6hebsrYgbz8hJwUQao3TWCMtmfV8Nu1twOLAw=="],
 
-    "@lovable.dev/cloud-auth-js": ["@lovable.dev/cloud-auth-js@1.1.2", "https://europe-west1-npm.pkg.dev/lovable-core-prod/sandbox-npm-cache/@lovable.dev/cloud-auth-js/-/cloud-auth-js-1.1.2.tgz", {}, "sha512-xz8ocewsgwkp8giau272/eWWU3XrchCg5uba4yQPPYtevHTXaVU3sD+fO1JjyPBHacVcOcwhmgUiU9TKHt63cg=="],
-
     "@lovable.dev/vite-plugin-dev-server-bridge": ["@lovable.dev/vite-plugin-dev-server-bridge@1.0.2", "", { "peerDependencies": { "vite": ">=5.0.0 <9.0.0" } }, "sha512-1c4XLFkpS614VxPyq+IX0us52vm5JWxdO1NfG2L1FjH0asKvHNu5//6wpnKHWmx60Y4HR1gcLaIiLACXIdeFyg=="],
 
     "@lovable.dev/vite-plugin-hmr-gate": ["@lovable.dev/vite-plugin-hmr-gate@1.1.1", "https://europe-west1-npm.pkg.dev/lovable-core-prod/sandbox-npm-cache/@lovable.dev/vite-plugin-hmr-gate/-/vite-plugin-hmr-gate-1.1.1.tgz", { "peerDependencies": { "vite": ">=5.0.0 <9.0.0" } }, "sha512-ySRUzOoGQYhj4Pd9EjaA7i1+2RiaS5lSVZasun72wVZZmJfFIciGYGQQDUu88HISn4icz0sugQxFRJGCNlTggg=="],