Refactor App.tsx from god component to context-based architecture

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/web/src/contexts/encounter-context.tsx

@@ -0,0 +1,21 @@
+import { createContext, type ReactNode, useContext } from "react";
+import { useEncounter } from "../hooks/use-encounter.js";
+
+type EncounterContextValue = ReturnType<typeof useEncounter>;
+
+const EncounterContext = createContext<EncounterContextValue | null>(null);
+
+export function EncounterProvider({ children }: { children: ReactNode }) {
+	const value = useEncounter();
+	return (
+		<EncounterContext.Provider value={value}>
+			{children}
+		</EncounterContext.Provider>
+	);
+}
+
+export function useEncounterContext(): EncounterContextValue {
+	const ctx = useContext(EncounterContext);
+	if (!ctx) throw new Error("useEncounterContext requires EncounterProvider");
+	return ctx;
+}