Carry conversations into new sessions with a visible summary

- Bots get continue_in_new_session: the bot writes a title and summary,
  the session closes for good (read-only) and the new one opens with the
  summary as a "Carried over from the last session" message that links
  back to the old session.
- Continue in new session (conversation menu, sessions modal) and the
  automatic rollover at the session length do the same; New session now
  starts a fresh, unlinked session.
- Session length is an app setting in Settings > General.
- ?session_id= opens a session; a carried-over one shows a bar linking to
  where the conversation went on instead of the composer.
- The thread can open the previous session above the current one (shown
  only, never in the prompt), and replies get search_past_sessions and
  read_past_session.
- Sessions are named from their opening messages, not their latest, and
  a carried summary is labelled as the earlier session's.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

db/schema.ts

@@ -464,6 +464,11 @@ const schema: BUN_SQLITE_DatabaseSchemaType = {
                     fieldDescription: `JSON \`[{ name, ok }]\`: every tool call the run behind a bot message made (names only, never arguments), told to the bot with the message in later turns so it can't build on work it never did. Null: not recorded (user messages, interim ones, older messages)`,
                     dataType: "TEXT",
                 },
+                {
+                    fieldName: "carried_from_session_id",
+                    fieldDescription: `Set on the message that opens a session the bot moved the conversation into (\`continue_in_new_session\`): the session it carries on from, whose summary is the message's text. Not a foreign key`,
+                    dataType: "INTEGER",
+                },
             ],
             indexes: [
                 {