fix(web): record which preset a session actually runs

The creation header names the preset a session STARTED with and is frozen,
which is correct — it is a creation fact. Switching is legal only while a
session is blank, and that looked like enough: no history exists yet.

It is not, because the switch's effect outlives the blank window. The user
switches, then sends the first message; every turn from there runs under the
new composition while the header still names the old one. The session is
then locked around a misrecorded preset, and resume reads the header to
rebuild it — composing one preset's tools over a history another produced,
which is exactly the replay the blank-only lock exists to prevent, reached
by another route. A picker showed `standard` for a session running
`core-web`.

A switch is now an `agent-preset/selected` event appended after the swap
commits, and `resolveSessionPreset()` (last selection, else the header) is
what every reconstruction reads: the summary, resume, the conflict guard,
and the fork introduced one layer down.

packages/preset/agent-presets/README.md

@@ -21,6 +21,12 @@ Discovery is unmemoized: `list()` and `resolve()` re-read the roots on every cal
 
 The agent factory's `setup(agentCtx)` hook is the one supported call site. Only there is the composition installed while the agent is still unpublished, so a rejected mount rolls the whole creation back rather than leaving a half-composed session. The subtree is owned by `agentCtx`'s fiber, so it unwinds with the agent and the caller receives no disposer.
 
+### Which preset a session runs
+
+The creation header names the preset a session STARTED with; `resolveSessionPreset(session)` names the one it RUNS. They differ whenever a blank session switched, so every reconstruction path — the summary a picker reads, a resume, a fork — resolves rather than reading the header.
+
+The header stays frozen because it is a creation fact. A switch is an `agent-preset/selected` session event appended after the swap commits, which is what the model-visible ⟺ logged rule requires: the preset decides the tool schemas and prompt sections the model sees, so it has to be reconstructable from the log. Reading the header alone would rebuild a switched session under the composition it was created with, replaying history the new tool set cannot act on — the exact hazard the blank-only lock exists to prevent.
+
 ## Config
 
 | Field | Default | Meaning |