[FEATURE] Dispatch mobile: allow selecting and copying text from Claude's responses

Problem

In Dispatch on the Claude mobile app, I can't select or copy text from Claude's responses. I often need a piece of a reply somewhere else, like a command, a path, a paragraph or a draft message, and the only way to get it is to retype it or wait until I'm back at the desktop.

Proposed solution

Make Dispatch responses selectable and copyable on mobile, the same way they are in a regular Claude chat:

• long-press to select part of a response, with the normal selection handles
• a "Copy" action for the whole message
• a copy button on code blocks

Related

#71718 reported the same problem for the Code tab (Remote Control sessions) on mobile. It was auto-closed for inactivity rather than fixed, and it's now locked, so I'm opening a new issue here as the bot suggested.