feat: add web search and background process tools (Phases 4-5)

Phase 4 - Web search tool:
- Brave Search API + SearXNG fallback
- Configurable provider, max results
- 14 tests

Phase 5 - Background process management:
- ProcessManager with start/status/output/kill/list tools
- Configurable max concurrent, max runtime, buffer size
- 28 tests

src/tools/builtin/process/status.ts

@@ -0,0 +1,42 @@
+import type { Tool, ToolResult } from '../../types.js';
+import type { ProcessManager } from './manager.js';
+
+interface ProcessStatusArgs {
+  id: string;
+}
+
+export function createProcessStatusTool(manager: ProcessManager): Tool {
+  return {
+    name: 'process.status',
+    description: 'Check the status of a background process by its ID.',
+    inputSchema: {
+      type: 'object',
+      properties: {
+        id: { type: 'string', description: 'Process ID (e.g. "proc_1")' },
+      },
+      required: ['id'],
+    },
+    execute: async (rawArgs: unknown): Promise<ToolResult> => {
+      const args = rawArgs as ProcessStatusArgs;
+      const proc = manager.get(args.id);
+      if (!proc) {
+        return { success: false, output: '', error: `Process ${args.id} not found` };
+      }
+
+      const uptime = proc.status === 'running'
+        ? `${Math.round((Date.now() - proc.startedAt) / 1000)}s`
+        : 'N/A';
+
+      let info = `Process: ${proc.id}\n`;
+      info += `Command: ${proc.command}\n`;
+      info += `PID: ${proc.pid}\n`;
+      info += `Status: ${proc.status}\n`;
+      info += `Uptime: ${uptime}\n`;
+      if (proc.exitCode !== undefined) info += `Exit code: ${proc.exitCode}\n`;
+      if (proc.errorMessage) info += `Error: ${proc.errorMessage}\n`;
+      if (proc.cwd) info += `CWD: ${proc.cwd}\n`;
+
+      return { success: true, output: info.trimEnd() };
+    },
+  };
+}