chore: cleanup context window ui, adjust for reasoning + added db migration

lib/db/schema.ts

@@ -4,6 +4,7 @@ import {
   varchar,
   timestamp,
   json,
+  jsonb,
   uuid,
   text,
   primaryKey,
@@ -29,6 +30,7 @@ export const chat = pgTable('Chat', {
   visibility: varchar('visibility', { enum: ['public', 'private'] })
     .notNull()
     .default('private'),
+  lastContext: jsonb('lastContext'),
 });
 
 export type Chat = InferSelectModel<typeof chat>;