[BUG] Desktop app: input draft loses markdown formatting after switching session tabs

Bug

A formatted markdown bullet list typed into the prompt input box reverts to raw markdown (literal * characters, no rendered bullets or indentation) after switching to another session's tab and switching back.

Steps to reproduce

1. Type a markdown bullet list in the input box, e.g.:

```

• im formatted bullet list
• bla bla
• double bla

```
The input renders it as a formatted, indented list.

1. Switch to another session's tab.
2. Switch back to the original session.
3. The draft now shows the raw * markdown — formatting is lost.

Expected

The draft keeps its rendered formatting when switching tabs and back.

Actual

The draft re-renders as raw, unformatted markdown text.

Environment

• Surface: Claude Code Desktop app
• OS: macOS (Darwin 25.5)
• App version: Claude 1.15962.1 (1e236d) 2026-06-26T19:44:44.000Z

Notes

Reproducible every time. Screenshots of before (formatted) and after (raw) available on request.