fix(cli): clear screen before spawning child process

Prevents Vite startup logs and connection messages from mixing
with the TUI app's output.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

packages/cli/src/process-manager.ts

@@ -16,6 +16,7 @@ export function createProcessManager(options: ProcessManagerOptions) {
   let currentBundlePath = options.bundlePath;
 
   function doSpawn() {
+    process.stdout.write("\x1b[2J\x1b[H");
     options.logger.mode = "silent";
     child = spawn("node", ["--import", loaderBootstrap, currentBundlePath], {
       stdio: "inherit",