Name sessions with the model and keep the rail list live

Sessions no longer take their title from the first message: once the first exchange is sent, the text model writes the title and summary, which the rail and sessions list show. The summary records how many messages it covers so a stale one is rewritten before it is carried into the next session.

The sessions hook now reloads on live message and session events, so a session started by the first message, a rollover or another tab appears without a reload. New sessions are pushed as server:bot-session, both from the process that changed them and through the live relay.

db/schema.ts

@@ -305,14 +305,19 @@ const schema: BUN_SQLITE_DatabaseSchemaType = {
                 },
                 {
                     fieldName: "title",
-                    fieldDescription: `From the first user message`,
+                    fieldDescription: `Written by the bot from the session's first exchange`,
                     dataType: "TEXT",
                 },
                 {
                     fieldName: "summary",
-                    fieldDescription: `What happened in the session (markdown), written by the bot when the next one starts and carried into it`,
+                    fieldDescription: `What happened in the session (markdown), written by the bot and refreshed as it goes, then carried into the next one`,
                     dataType: "TEXT",
                 },
+                {
+                    fieldName: "summary_message_count",
+                    fieldDescription: `How many of the session's messages the summary covers, so a stale one is rewritten before it's carried into the next session`,
+                    dataType: "INTEGER",
+                },
                 {
                     fieldName: "previous_session_id",
                     fieldDescription: `The session this one carries on from (its summary goes into the prompt). Not a foreign key`,