@ file mention only searches directory names, never file names

Description

The @ file mention in the prompt input only fuzzy-matches against directory names — it never matches file names.

Repro

1. Open any project.
2. Create a new file, e.g. FooBar.ts.
3. Type @FooBar in the prompt input.
4. Expected: FooBar.ts appears in the mention list.
5. Actual: it does not appear.

Root cause

packages/app/src/context/file.tsx maps searchFilesAndDirectories to the backend find with type: "directory", so the server only searches the directory index.

This is a regression from the v2 migration (feat(app): migrate discovery workflows): the old client find.files({ dirs: true }) searched files + directories, but the new mapping collapsed it to directories only.

Verified against the core search service:

type=file       -> can find the new file
type=directory  -> empty
type=undefined  -> can find it (files + directories mixed)

Related issues

• #38065, #32747 — @ autocomplete does not detect newly created files. This issue is a distinct code-level cause that also contributes to that symptom (the search only ever queries directory names, so no newly created file is ever matched by filename).

Suggested fix

searchFilesAndDirectories should omit type so the server runs the mixed (file + directory) search; the server find already treats type === undefined as files + directories.