[FEATURE] Pinned inline threads: ask about a selected part of Claude's reply without derailing the conversation

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

I work in the Claude desktop app with several Code sessions open at once, each on one topic. While reading a long reply I constantly need small clarifications: what a term means in two words, whether a fact came from my own files or from the web, or a quick instruction like "don't use this wording from now on".

The only place to ask is the main input at the bottom. That pulls the conversation off its central thread, and Claude often follows the tangent far away from the main topic. Later, when I scroll back, those clarifications are buried in the main flow, and I can no longer see which part of the text they were about.

### Proposed Solution

Select any part of Claude's reply, right-click, choose "Ask about this". A small popup thread opens, anchored to that selection, with a close button.

- I type my question in the popup, and Claude answers in the same popup.
- The popup stays attached to the selected text and scrolls together with it.
- A closed thread leaves a small marker on the text, so I can reopen it later.
- When I scroll back through the conversation, I see what I clarified and the answer right next to the text it was about.
- The main conversation stays on topic, but Claude takes these clarifications into account in its next answers - an instruction like "don't use this word" should stick.

### Alternative Solutions

- Asking in the main input: derails the topic and buries the clarification in the main flow.
- Forking the conversation: opens a new window and takes me out of context.
- Side chat (/btw, Cmd+;): the closest existing tool, but it is not anchored to a specific part of the reply, so the question and answer do not stay next to the text they were about.

### Priority

Critical - Blocking my work

### Feature Category

CLI commands and flags

### Use Case Example

1. In a long working session, Claude replies with a detailed summary.
2. One line uses a term I don't know; another cites a number, and I'm not sure whether it came from my files or from the web.
3. I select the term, right-click, and ask "explain in two words" - the answer appears in a small popup next to that line.
4. I select the number and ask "where is this from?" - the answer appears next to it too.
5. I continue the main discussion with no detour. A week later, scrolling back, I still see both clarifications pinned next to the text.

### Additional Context

Related but different requests:
- #91030 - VS Code: "Ask Claude about this selection" quotes the selection into the prompt box; there is no persistent pinned thread.
- #82103 - bring the Code tab's side chat to the Chat and Cowork tabs.
- #85674 - keep a log of /btw messages (closed).

This request is about the desktop app conversation view; the same pattern would be just as useful in claude.ai chat.

The request names no files, tests, or entry points. First confirm whether the desktop-app conversation view belongs in this repository, then locate the existing side chat (/btw, Cmd+;) implementation; done would include selection-anchored popup threads, persistent markers, scrolling with the text, and clarification context in later answers.

Written by the indexing model from the issue text.