Add bd exec bridge and mutation API routes with tests

src/app/api/beads/_shared.ts

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+import { NextResponse } from 'next/server';
+
+import { executeMutation, MutationValidationError, validateMutationPayload, type MutationOperation } from '../../../lib/mutations';
+
+function badRequest(message: string, operation: MutationOperation) {
+  return NextResponse.json(
+    {
+      ok: false,
+      operation,
+      error: {
+        classification: 'bad_args',
+        message,
+      },
+    },
+    { status: 400 },
+  );
+}
+
+export async function handleMutationRequest(request: Request, operation: MutationOperation): Promise<Response> {
+  let body: unknown;
+
+  try {
+    body = await request.json();
+  } catch {
+    return badRequest('Invalid JSON body.', operation);
+  }
+
+  try {
+    const payload = validateMutationPayload(operation, body);
+    const result = await executeMutation(operation, payload);
+
+    const status = result.ok ? 200 : result.error?.classification === 'not_found' ? 404 : 400;
+    return NextResponse.json(result, { status });
+  } catch (error) {
+    if (error instanceof MutationValidationError) {
+      return badRequest(error.message, operation);
+    }
+
+    return NextResponse.json(
+      {
+        ok: false,
+        operation,
+        error: {
+          classification: 'unknown',
+          message: error instanceof Error ? error.message : 'Unknown mutation error.',
+        },
+      },
+      { status: 500 },
+    );
+  }
+}

src/app/api/beads/close/route.ts

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+import { handleMutationRequest } from '../_shared';
+
+export async function POST(request: Request): Promise<Response> {
+  return handleMutationRequest(request, 'close');
+}

src/app/api/beads/comment/route.ts

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+import { handleMutationRequest } from '../_shared';
+
+export async function POST(request: Request): Promise<Response> {
+  return handleMutationRequest(request, 'comment');
+}

src/app/api/beads/create/route.ts

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+import { handleMutationRequest } from '../_shared';
+
+export async function POST(request: Request): Promise<Response> {
+  return handleMutationRequest(request, 'create');
+}

src/app/api/beads/reopen/route.ts

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+import { handleMutationRequest } from '../_shared';
+
+export async function POST(request: Request): Promise<Response> {
+  return handleMutationRequest(request, 'reopen');
+}

src/app/api/beads/update/route.ts

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+import { handleMutationRequest } from '../_shared';
+
+export async function POST(request: Request): Promise<Response> {
+  return handleMutationRequest(request, 'update');
+}