[FEATURE] Add /fork (conversation branching) support to JetBrains plugin

### Preflight Checklist

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

### Problem Statement

The CLI supports conversation forking via `--fork-session` / `/fork` / `/branch`, and it's already been requested for the VS Code extension (#69272). The JetBrains plugin (IntelliJ/PhpStorm/WebStorm/etc.) has no equivalent — there's no way to branch a session at a given point from within the JetBrains tool window the way Cursor supports forking a chat.

### Proposed Solution

Add `/fork` (or a UI action, e.g. a "Fork from here" option on a message) to the JetBrains plugin's Claude Code tool window, matching the CLI's forking behavior: branch the conversation at the selected point into a new session, preserving full history up to the fork point, while leaving the original session untouched.

### Priority

Medium

### Feature Category

JetBrains plugin (IntelliJ/PhpStorm)

### Additional Context

Related: #69272 (same request for VS Code extension).

No implementation files or tests are named. Start by locating the JetBrains plugin's Claude Code tool window and session handling, then compare the requested behavior with the CLI's /fork support and related VS Code request #69272. Done means a selected conversation point creates a new session with prior history while leaving the original untouched.

Written by the indexing model from the issue text.