[Feature] Add session fork support

[Ymaril]

Is your feature request related to a problem? Please describe.
Users may want to fork a session to branch off from existing conversation history while keeping the original intact.

Describe the solution you'd like
Add support for forking sessions through the UI. When a user forks a session, create a new independent session that continues from the original's conversation history.

Additional context
Claude's SDK supports session forking natively, which could be a good starting point for implementation.

[liran-funaro]

Worth knowing before anyone scopes this: the SDK already has fork, so the work is wiring rather than mechanism. Checked against CloudCLI v1.37.2 and Claude Code CLI 2.1.245.

@anthropic-ai/claude-agent-sdk exposes three ways in:

// standalone — copies a session, optionally sliced
forkSession(sessionId: string, options?: {
  dir?: string,
  upToMessageId?: string,   // slice transcript up to this message UUID (inclusive)
  title?: string,           // defaults to the original title + " (fork)"
}): Promise<{ sessionId: string }>   // resumable via query({ options: { resume: sessionId } })

// query option, when resuming
forkSession?: boolean

and the CLI itself has --fork-session ("when resuming, create a new session ID"), which is the same thing from the command line.

None of the three appears anywhere in the shipped server — zero occurrences of forkSession or fork-session — so there is nothing to build on, and equally nothing in the way.

Two shapes fall out of that API, and they cost very different amounts of UI:

1. Fork the whole session. forkSession(providerSessionId) → insert the returned id as a new session row in the same project → resume it as normal. The affordance can be one more item in the per-session menu that already carries rename / copy provider session id / archive / delete. No new UI surface at all.
2. Fork from a point in the conversation. Same call with upToMessageId, which is the interesting version — and the one that needs a message-level affordance, so it is the expensive half. It also pairs naturally with Add rewind support for Claude Code CLI #199 (rewind), since both are "go back to this message and continue differently".

I am not volunteering to implement it — I have no need for it myself — but (1) looked cheap enough that it seemed worth writing down rather than leaving the impression that the whole feature needs new UI.