fix: start a forked session so the client can prompt it at once (#1317)

## Problem

The v1 schema says a forked session is active once the agent responds,
and can be prompted without `session/load` or `session/resume`
(agentclientprotocol/agent-client-protocol#2359). `session/fork` only
copied the transcript, so prompting the new id failed with "Session not
found" until the client loaded or resumed it.

## Change

- **The fork starts the new session the way a resume does.** It starts
from the copied transcript, with the model and the permission mode that
transcript records, and with the request's `cwd`, MCP servers,
additional directories and `_meta`. The response carries the session's
`modes` and `configOptions`, and the available commands follow it, as
for `session/new`.
- **A client that loads or resumes after a fork keeps working.** A later
`session/load` replays the history into the running session, and a later
`session/resume` returns it. Neither starts a second Claude Code
process. A load or resume with other settings restarts the session, as
for any loaded session. The fingerprint that decides this ignores the
AIR fork point in `_meta`.
- **Cost:** each fork now starts a Claude Code process. That added about
0.65 s to the fork response in the live run.
- **v2:** the v2 fork used to resume the forked session itself. It now
uses the session that the v1 fork starts, so the v2 bridge drops its own
resume.
- **AIR docs:** `docs/air-extensions.md` now says, under the session
fork point, what a load or resume after a fork does.

## Evidence

**Live, CLI 2.1.293 on Haiku, over v1:**
1. A new session answered "Remember the codeword PELICAN" with `OK`.
2. `session/fork` returned the fork with mode `auto` and the `mode`,
`model` and `effort` config options.
3. Prompting the fork right away returned `PELICAN`, with no load or
resume in between.
4. A `session/load` of the fork then replayed its history and was ready
in 4 ms. The timing log shows one session start for the fork and none
for the load, and a further prompt still answered.

**Tests:**
- New: the fork can be prompted at once, and its response carries modes
and config options; a later resume and load reuse the session; and the
fork fails when its session can't start.
- The existing fork tests now also check that the session starts from
the fork, with the request's additional directories.
- The v2 fork tests pass unchanged.
- **Mutation checks:** removing the start, the response's `modes`, or
the additional directories each fails a test.
- `npm run check`, build and all 2813 tests pass, with no golden
changes.

docs/air-extensions.md

@@ -1541,6 +1541,8 @@ It adds this object to the `session/fork` request:
   When only one stored message has the fingerprint, the adapter uses that message.
 - When no message matches, the request fails with `invalidParams`.
 - The fork keeps the history up to that message.
+- With or without this object, the forked session runs once the response arrives, so the client can prompt it without `session/load` or `session/resume`.
+  A later load replays its history into it, and a later resume returns it. A load or resume with other settings (`cwd`, MCP servers, additional directories, or the session options in `_meta`) restarts it, as for any loaded session.
 
 ## Presentation hints