feat: live agent answers (SSE streaming) + «Чат» tab on phones

- POST /dialog/{token}/events/stream: Server-Sent Events with the agent's steps («Смотрю вашу карту ЕМИАС…»,
  «Ищу в клинических рекомендациях…»), the answer as the model writes it (OpenRouter stream=true), then the
  final replies (same as /events, incl. the forbidden-output filter and sources). X-Accel-Buffering: no.
- Web: free-text messages use the stream — a live bubble with steps, typing dots and a cursor; falls back to
  the plain request if the stream breaks.
- Phones: the bottom tab bar gets «Чат» (it had no way back to the chat).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

web/src/dialog/DialogContext.tsx

@@ -1,6 +1,6 @@
 import { createContext, useCallback, useContext, useEffect, useMemo, useRef, useState, type ReactNode } from "react";
 
-import { api } from "../api/client";
+import { api, sendEventStream } from "../api/client";
 import type { DialogEvent, Reply } from "../api/types";
 import { useSession } from "../session/SessionContext";
 import { sessionStore, type ChatEntry, type DialogSnapshot } from "../session/store";
@@ -17,8 +17,15 @@ let seq = 0;
 const newId = () => `${Date.now().toString(36)}-${(seq++).toString(36)}`;
 const asEntries = (replies: Reply[]): ChatEntry[] => replies.map((reply) => ({ id: newId(), from: "assistant", reply }));
 
+/** The agent at work: its steps and the answer as it is being written (cleared when the final reply lands). */
+export interface LiveReply {
+  status: string[];
+  text: string;
+}
+
 interface DialogApi extends DialogSnapshot {
   busy: boolean;
+  live: LiveReply | null;
   error: boolean;
   started: boolean;
   /** Sends an event; `echo` is what the patient «said» (button label / text) for the history. */
@@ -36,6 +43,7 @@ export function DialogProvider({ children }: { children: ReactNode }) {
   const [owner, setOwner] = useState(token);
   const [snap, setSnap] = useState<DialogSnapshot>(() => (token ? sessionStore.loadDialog(token) : EMPTY));
   const [busy, setBusy] = useState(false);
+  const [live, setLive] = useState<LiveReply | null>(null);
   const [error, setError] = useState(false);
   const tokenRef = useRef(token);
   tokenRef.current = token;
@@ -58,7 +66,35 @@ export function DialogProvider({ children }: { children: ReactNode }) {
       setBusy(true);
       setError(false);
       try {
-        const replies = await api.sendEvent(t, event);
+        let replies: Reply[];
+        if (event.type === "text") {
+          // Free text may go to the agent: stream its steps and the answer so the viewer sees it working.
+          const said = echo;
+          if (said) {
+            // Show the patient's message right away, while the agent is still working.
+            setSnap((prev) => ({
+              ...prev,
+              entries: [...prev.entries, { id: newId(), from: "patient" as const, text: said }],
+            }));
+            echo = undefined;
+          }
+          setLive({ status: [], text: "" });
+          try {
+            replies = await sendEventStream(t, event, (e) =>
+              setLive((prev) => {
+                const cur = prev ?? { status: [], text: "" };
+                if (e.kind === "status") return { ...cur, status: [...cur.status, e.text] };
+                if (e.kind === "delta") return { ...cur, text: cur.text + e.text };
+                if (e.kind === "reset") return { ...cur, text: "" };
+                return cur;
+              }),
+            );
+          } catch {
+            replies = await api.sendEvent(t, event); // proxies without SSE support: plain request
+          }
+        } else {
+          replies = await api.sendEvent(t, event);
+        }
         setSnap((prev) => ({
           entries: [
             ...prev.entries,
@@ -73,6 +109,7 @@ export function DialogProvider({ children }: { children: ReactNode }) {
         setError(true);
         return false;
       } finally {
+        setLive(null);
         setBusy(false);
       }
     },
@@ -102,8 +139,8 @@ export function DialogProvider({ children }: { children: ReactNode }) {
   }, [token]);
 
   const value = useMemo<DialogApi>(
-    () => ({ ...snap, busy, error, started: snap.entries.length > 0, send, start, markRead }),
-    [snap, busy, error, send, start, markRead],
+    () => ({ ...snap, busy, live, error, started: snap.entries.length > 0, send, start, markRead }),
+    [snap, busy, live, error, send, start, markRead],
   );
   return <Ctx.Provider value={value}>{children}</Ctx.Provider>;
 }