feat: the assistant's talk is kept in the database per user and the model sees a trimmed window of it; clear is a broom; the ball steps aside for the chat and comes back where the chat was

internal/server/web/static/app.css

@@ -888,3 +888,8 @@ body:not(.touch) .ai-fab { cursor:grab; touch-action:none; }
   body.touch.term-active .ai-fab { bottom:110px; }
   .ai-form-in textarea { font-size:16px; }
 }
+.ai-clear { width:30px; height:30px; padding:0; display:inline-flex; align-items:center; justify-content:center; }
+/* The ball steps aside while the chat is open, and back when it shuts. */
+.ai-fab { transition:transform .22s ease, opacity .22s ease, box-shadow .2s ease, right .25s ease, bottom .25s ease; }
+.ai-fab.away { opacity:0; transform:scale(.5); pointer-events:none; }
+body.ai-dragging .ai-fab, body.ai-dragging .ai-box { transition:none; }