feat: add internal AI chat assistant and AI Input Agent page

- Add Gemini-powered internal staff chatbot (free-text input in the
  upper-right bot panel): type "check MARIA GONZALES" to search patient
  and pre-fill eligibility, or "open claims" to navigate directly
- Add /api/ai/internal-chat endpoint with LangGraph + Google Gemini
  classifier (intent: check_eligibility, find_patient, navigate_*)
- Add Users AI Chat settings section in Settings > Advanced > AI Chat
  to configure a custom system prompt for the internal assistant
- Store internal chat system prompt in existing twilioSettings JSON
  blob (no DB migration needed)
- Add AI Input Agent sidebar entry and placeholder page describing
  planned keyboard-automation typing into Open Dental / Eaglesoft

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

apps/Backend/src/ai/internal-chat-graph.ts

@@ -0,0 +1,69 @@
+import { ChatGoogleGenerativeAI } from "@langchain/google-genai";
+
+export type InternalChatIntent =
+  | "check_eligibility"
+  | "find_patient"
+  | "navigate_claims"
+  | "navigate_schedule"
+  | "general";
+
+export interface ChatClassification {
+  intent: InternalChatIntent;
+  patientName?: string;
+  fallbackReply: string;
+}
+
+const BASE_SYSTEM_PROMPT = `You are an internal assistant for a dental office management system.
+Staff members type natural language commands and you classify what they want.
+
+Respond ONLY with valid JSON (no markdown, no code fences) in this exact format:
+{
+  "intent": "<one of the intents below>",
+  "patientName": "<full name if patient is mentioned, otherwise omit>",
+  "fallbackReply": "<a short, helpful reply to show the user>"
+}
+
+Intents:
+- check_eligibility: user wants to check insurance eligibility for a patient (e.g. "check MARIA", "verify insurance for John Smith", "eligibility GONZALES")
+- find_patient: user wants to look up a patient record only (e.g. "find patient John", "look up Smith", "show me GONZALES record")
+- navigate_claims: user wants to open the claims page
+- navigate_schedule: user wants to open the appointments/schedule page
+- general: anything else — answer helpfully based on dental office context
+
+Rules:
+- Extract the full patient name as-is from the message for check_eligibility and find_patient
+- Keep fallbackReply to 1-2 sentences max
+- For navigate intents, fallbackReply should say "Opening the [page] page..."`;
+
+export async function classifyInternalChat(
+  message: string,
+  apiKey: string,
+  extraSystemPrompt?: string
+): Promise<ChatClassification> {
+  const fallback: ChatClassification = {
+    intent: "general",
+    fallbackReply: "I can help you search for a patient, check eligibility, or navigate to claims or appointments.",
+  };
+
+  if (!apiKey) return fallback;
+
+  const systemPrompt = extraSystemPrompt
+    ? `${BASE_SYSTEM_PROMPT}\n\nAdditional office context:\n${extraSystemPrompt}`
+    : BASE_SYSTEM_PROMPT;
+
+  try {
+    const llm = new ChatGoogleGenerativeAI({ model: "gemini-1.5-flash", apiKey });
+    const response = await llm.invoke([
+      { role: "system", content: systemPrompt },
+      { role: "user", content: message },
+    ]);
+
+    const raw = String(response.content).trim();
+    const jsonStr = raw.replace(/^```json\s*/i, "").replace(/```\s*$/, "").trim();
+    const parsed = JSON.parse(jsonStr) as ChatClassification;
+    if (!parsed.intent || !parsed.fallbackReply) return fallback;
+    return parsed;
+  } catch {
+    return fallback;
+  }
+}