feat(web): choose the agent preset on the new-session screen

The composer seat spent nearly all its life disabled: a session's
composition is fixed once a turn has run. Move the choice to the
new-session screen beside the workspace picker, where it still works,
and let the session header report what a running session runs.

The hero pick is staged rather than applied — that screen precedes the
session it belongs to. It lands when a session becomes current and is
still blank, which covers both the session a workspace connect creates
and the blank one it reuses; riding `sessions.create` would miss the
second. It is spent on first use, matching the workspace picker.

Fix the durability the header field claimed but never had: `agentPreset`
was declared on `SessionHeader` and dropped by the JSONL header line, the
SQLite sessions row, the derived query index, and the cold list
projection, so every resumed session came back composed from nothing.

Add the web e2e lane that would have caught it — the one lane that mounts
the shipped roster, which needed `cordis:group` in the scaffold's Loader
builtins, as `mountRootInclude` already registers.

packages/host/apiproxy/src/api-proxy.ts

@@ -328,12 +328,10 @@ async function summarizeCold(
     // a cold log to check for turns would defeat the index read, so a listed
     // cold session is served as not-blank (its log holds its conversation).
     blank: false,
-    ...meta.parentSession === undefined ? {} : { parentSessionId: meta.parentSession },
-    ...meta.origin === undefined ? {} : { origin: meta.origin },
-    /* v8 ignore next -- the empty arm needs a cwd-less meta, but list()
-    filters those out (legacy logs are not served); the conditional mirrors
-    summarize() shape. */
-    ...meta.cwd === undefined ? {} : { cwd: meta.cwd },
+    // Header-only: reading the log for a blank-window preset switch would
+    // defeat the same index read, and attaching the session replaces this row
+    // with `summarize()`, which resolves the switch from the events.
+    ...sessionListFields(meta),
   }
 }