fix(web): fix stale state bugs, add real-time updates, and build verification pipeline

- Fix kanban board columns not adapting to available width (w-64 → flex-1)
- Fix workspace name not updating in sidebar after save in settings
- Fix comments leaking across issues when navigating between issue details
- Fix duplicate issue appearing on create (race between callback and WebSocket)
- Add real-time WebSocket listeners for agents and inbox pages
- Add `make check` one-click verification pipeline (typecheck + tests + E2E)
- Add E2E test fixtures for self-contained test data setup/teardown
- Add settings E2E test and updateWorkspace unit test
- Make `make start/setup` reuse existing PostgreSQL if already running
- Update CLAUDE.md with AI agent verification loop and E2E test patterns

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

e2e/fixtures.ts

@@ -0,0 +1,70 @@
+/**
+ * TestApiClient — lightweight API helper for E2E test data setup/teardown.
+ *
+ * Uses raw fetch (no dependency on @multica/sdk build) so E2E tests
+ * have zero build-time coupling to monorepo packages.
+ */
+
+const API_BASE = "http://localhost:8080";
+
+export class TestApiClient {
+  private token: string | null = null;
+  private workspaceId: string | null = null;
+  private createdIssueIds: string[] = [];
+
+  async login(email: string, name: string) {
+    const res = await fetch(`${API_BASE}/auth/login`, {
+      method: "POST",
+      headers: { "Content-Type": "application/json" },
+      body: JSON.stringify({ email, name }),
+    });
+    const data = await res.json();
+    this.token = data.token;
+    return data;
+  }
+
+  async getWorkspaces() {
+    const res = await this.authedFetch("/api/workspaces");
+    return res.json();
+  }
+
+  setWorkspaceId(id: string) {
+    this.workspaceId = id;
+  }
+
+  async createIssue(title: string, opts?: Record<string, unknown>) {
+    const res = await this.authedFetch("/api/issues", {
+      method: "POST",
+      body: JSON.stringify({ title, ...opts }),
+    });
+    const issue = await res.json();
+    this.createdIssueIds.push(issue.id);
+    return issue;
+  }
+
+  async deleteIssue(id: string) {
+    await this.authedFetch(`/api/issues/${id}`, { method: "DELETE" });
+  }
+
+  /** Clean up all issues created during this test. */
+  async cleanup() {
+    for (const id of this.createdIssueIds) {
+      try {
+        await this.deleteIssue(id);
+      } catch {
+        /* ignore — may already be deleted */
+      }
+    }
+    this.createdIssueIds = [];
+  }
+
+  private async authedFetch(path: string, init?: RequestInit) {
+    const headers: Record<string, string> = {
+      "Content-Type": "application/json",
+      ...((init?.headers as Record<string, string>) ?? {}),
+    };
+    if (this.token) headers["Authorization"] = `Bearer ${this.token}`;
+    if (this.workspaceId) headers["X-Workspace-ID"] = this.workspaceId;
+    return fetch(`${API_BASE}${path}`, { ...init, headers });
+  }
+}