fix(extension): pass client name on token-bypass connect

[cipheraxat]

Summary

• On the token-bypass connect path, handleConnectToTab was called in the same effect that called setClientInfo(info), so it still closed over the initial "unknown" client name.
• Pass the freshly parsed client name into handleConnectToTab at that call site so the status page and tab group show the real MCP client name.
• Extend the existing token-bypass extension test to assert Connected to "token-bypass-client" on the status page.

Fixes #41839

Test plan

• npm run test-extension -- --grep "bypass connection" (chromium + legacy v1)
• Full npm run test-extension suite (2 unrelated flaky tab tests failed once, passed on rerun; bypass tests passed)

[yury-s]

This is just a band-aid both of clientNameOverride and clientInfo are the same, so this is a workaround for the react stale closure bug.

The client name comes from window.location.search, which never changes for the lifetime of the page. Let's parse it once outside the component (or in a useMemo) and use it as a plain constant:

const clientInfo = (() => {
  try {
    return JSON.parse(new URLSearchParams(window.location.search).get('client') || '{}').name || 'unknown';
  } catch {
    return 'unknown';
  }
})();

[cipheraxat]

Updated @yury-s per review feedback: clientInfo is now parsed once from window.location.search as a module-level constant, and the clientNameOverride workaround is removed. Bypass connection tests still pass.