feat: consolidate web auth and add Effect v4 Project primitives

Auth:
- Add useWebAuth hook as the single web-facing auth interface with four
  states (loading/unauthenticated/authenticated/inconsistent)
- Normalize getCurrentUser to return {id: tokenIdentifier, name, email}
- Rename requireOwnerId to requireAuthUserId across all backend callers
- Set expectAuth:true on ConvexReactClient singleton
- Migrate _app, _auth, user-menu, use-personal-organization to useWebAuth
- Remove unused @code/auth/server export (zero callers confirmed)

Primitives:
- Add packages/primitives/src/project.ts with Effect v4 Project domain:
  URL normalization, six canonical context kinds, strict remote decoding,
  context write decisioning with revision tracking, and no-op detection
- Define PublicGit and ProjectStore replaceable ports
- Define ProjectApplication service orchestrating domain+ports with
  deterministic error mapping
- Add comprehensive test suite (28 tests) with in-memory store and fake
  PublicGit covering normalization, seeds, idempotency, tenant isolation,
  last-write-wins, and typed error mapping

packages/auth/package.json

@@ -5,7 +5,6 @@
   "type": "module",
   "exports": {
     "./native": "./src/native/index.ts",
-    "./server": "./src/server/index.ts",
     "./web": "./src/web/index.ts"
   },
   "scripts": {

packages/auth/src/server/index.ts

@@ -1 +0,0 @@
-export { authComponent, createAuth } from "@code/backend/convex/auth";

packages/auth/src/web/auth-provider.tsx

@@ -5,7 +5,7 @@ import type { ReactNode } from "react";
 
 import { authClient } from "./auth-client";
 
-const convex = new ConvexReactClient(env.VITE_CONVEX_URL);
+const convex = new ConvexReactClient(env.VITE_CONVEX_URL, { expectAuth: true });
 
 export const WebAuthProvider = ({ children }: { children: ReactNode }) => (
   <ConvexBetterAuthProvider authClient={authClient} client={convex}>

packages/auth/src/web/index.ts

@@ -1,5 +1,7 @@
 export { authClient } from "./auth-client";
 export { WebAuthProvider } from "./auth-provider";
 export { useConvexAccessToken } from "./hooks";
+export { signOutWeb, useWebAuth } from "./use-web-auth";
+export type { WebAuthState, WebAuthUser } from "./use-web-auth";
 export { LoginForm } from "./login-form";
 export { SignupForm } from "./signup-form";

packages/auth/src/web/use-web-auth.ts

@@ -0,0 +1,81 @@
+import { api } from "@code/backend/convex/_generated/api";
+import { useEffect, useRef } from "react";
+import { useConvexAuth, useQuery } from "convex/react";
+
+import { authClient } from "./auth-client";
+
+export interface WebAuthUser {
+  readonly id: string;
+  readonly name: string;
+  readonly email: string;
+}
+
+export type WebAuthState =
+  | { readonly status: "loading" }
+  | { readonly status: "unauthenticated" }
+  | { readonly status: "authenticated"; readonly user: WebAuthUser }
+  | { readonly status: "inconsistent" };
+
+/**
+ * Sign out of the web session. Clears the Better Auth session, which in turn
+ * invalidates the cached Convex JWT (the session-token resolver keys on the
+ * session id). Protected Convex queries after sign-out are denied.
+ */
+export const signOutWeb = async (): Promise<void> => {
+  await authClient.signOut({ fetchOptions: { throw: false } });
+};
+
+/**
+ * The single web-facing auth interface. Combines Convex auth state with the
+ * normalized {@link api.auth.getCurrentUser} projection, skipping the user
+ * query until Convex has authenticated. Reports `inconsistent` only when a JWT
+ * is accepted but the Better Auth user row cannot be resolved.
+ */
+export const useWebAuth = (): WebAuthState => {
+  const { isAuthenticated, isLoading } = useConvexAuth();
+
+  // Skip the user query until Convex has accepted the JWT. This keeps the
+  // status `loading` during token restoration and `unauthenticated` when no
+  // session exists, without firing a query that would return null.
+  const userQuery = useQuery(
+    api.auth.getCurrentUser,
+    isAuthenticated ? {} : "skip"
+  );
+
+  const signOutWebRef = useRef(signOutWeb);
+  const inconsistent =
+    isAuthenticated && userQuery !== undefined && userQuery === null;
+
+  // If Convex accepted the JWT but the Better Auth user row cannot be resolved,
+  // the session is inconsistent: sign out so the next sign-in starts clean.
+  useEffect(() => {
+    if (inconsistent) {
+      void signOutWebRef.current();
+    }
+  }, [inconsistent]);
+
+  if (isLoading) {
+    return { status: "loading" };
+  }
+
+  if (!isAuthenticated) {
+    return { status: "unauthenticated" };
+  }
+
+  if (userQuery === undefined) {
+    return { status: "loading" };
+  }
+
+  if (userQuery === null) {
+    return { status: "inconsistent" };
+  }
+
+  return {
+    status: "authenticated",
+    user: {
+      email: userQuery.email,
+      id: userQuery.id,
+      name: userQuery.name,
+    },
+  };
+};