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/session-persistence/session-persistence-sqlite/tests/sqlite.spec.ts

@@ -172,6 +172,7 @@ describe('rowToMeta', () => {
       incarnation: 'with-origin',
       revision: 1,
       delegation_depth: null,
+      agent_preset: null,
     })).toMatchObject({ id: 'with-origin', origin: 'subagent' })
   })
 
@@ -187,8 +188,27 @@ describe('rowToMeta', () => {
       incarnation: 'fractional',
       revision: 1,
       delegation_depth: null,
+      agent_preset: null,
     })).toThrow('stored session createdAt must be a non-negative safe integer')
   })
+
+  it('restores the agent preset a session was composed from', () => {
+    // The preset decides the resumed session's tools and prompt; a row that
+    // dropped it would rebuild a composition the stored history contradicts.
+    expect(rowToMeta({
+      id: 'composed',
+      version: 0,
+      created_at: 1,
+      cwd: null,
+      parent_session: null,
+      seed_length: null,
+      origin: null,
+      incarnation: 'composed',
+      revision: 1,
+      delegation_depth: null,
+      agent_preset: 'minimal',
+    })).toMatchObject({ agentPreset: 'minimal' })
+  })
 })
 
 describe('SessionPersistenceSqlite: durability and crash semantics', () => {
@@ -638,7 +658,7 @@ describe('SessionPersistenceSqlite: durability and crash semantics', () => {
   })
 
   it('exposes the schema version constant', () => {
-    expect(SCHEMA_VERSION).toBe(13)
+    expect(SCHEMA_VERSION).toBe(14)
   })
 
   it('keeps the revision stable for an empty repair hook', async () => {