Render inline code and code fences in the TUI input composer

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

The Claude Code TUI's input composer shows raw markdown syntax (backticks, code fences) while typing. The Desktop app already renders these live in its composer — see #57268 — so this is a TUI parity request, not new behaviour.

I frequently wrap variable names, file paths, and flags in backticks to disambiguate them in prompts. Without live rendering, the only way to confirm I didn't drop a backtick (e.g. miss a closing one) is to send the message and inspect the rendered bubble — one round-trip per check.

Proposed Solution

In the TUI input composer, render:

1. Inline code — ` foo ` with a distinct background or font weight.
2. Fenced code blocks — ``` ` ``` as a monospace block.

Scope deliberately small: no lang on code blocks ; no headings, lists, tables, or other CommonMark.

Alternative Solutions

• Compose in an external editor and paste — breaks the interactive flow.
• Send, inspect, edit — current workaround, costs a round-trip per typo.

Priority

Low - Nice to have

Feature Category

Interactive mode (TUI)

Use Case Example

While typing a prompt that references specific CLI flags (e.g. --include-prs, --body-file) or paths, I want immediate visual confirmation they are wrapped as inline code — rather than realising after submit that I dropped a closing backtick.

Additional Context

Display-layer change only; the backend already accepts markdown in user messages.