feat(bot,frontend,backend): add integration with external collaborative solver

frontend/src/routes/[mnemonic]/+page.svelte

@@ -20,6 +20,7 @@
 	import PhotoPreview from '$lib/components/PhotoPreview.svelte';
 	import DraftBadge from '$lib/components/DraftBadge.svelte';
 	import SilentCapture from '$lib/components/SilentCapture.svelte';
+	import IncomingSheetsPanel from '$lib/components/IncomingSheetsPanel.svelte';
 
 	const usePolling = getContext<boolean>('convex-use-polling') ?? false;
 	let mnemonic = $derived(page.params.mnemonic);
@@ -193,6 +194,38 @@
 	const photoDraft = $derived(usePolling ? photoDraftPoll! : photoDraftWs!);
 	const draftPhotos = $derived(photoDraft.data?.photos ?? []);
 
+	const incomingSheetsWs = usePolling
+		? null
+		: useQuery(api.incomingSheets.listForChat, () =>
+				chatId ? { chatId, status: 'preview' as const } : 'skip'
+			);
+	const incomingSheetsPoll = usePolling
+		? usePollingQuery(api.incomingSheets.listForChat, () =>
+				chatId ? { chatId, status: 'preview' as const } : 'skip'
+			)
+		: null;
+	const incomingSheetsQ = $derived(usePolling ? incomingSheetsPoll! : incomingSheetsWs!);
+	const incomingSheetItems = $derived(incomingSheetsQ.data ?? []);
+
+	const acceptSheetPoll = usePolling ? usePollingMutation(api.incomingSheets.accept) : null;
+	const dismissSheetPoll = usePolling ? usePollingMutation(api.incomingSheets.dismiss) : null;
+
+	function handleAcceptSheet(id: Id<'incomingSheets'>) {
+		if (usePolling && acceptSheetPoll) {
+			acceptSheetPoll({ id });
+		} else if (clientWs) {
+			clientWs.mutation(api.incomingSheets.accept, { id });
+		}
+	}
+
+	function handleDismissSheet(id: Id<'incomingSheets'>) {
+		if (usePolling && dismissSheetPoll) {
+			dismissSheetPoll({ id });
+		} else if (clientWs) {
+			clientWs.mutation(api.incomingSheets.dismiss, { id });
+		}
+	}
+
 	$effect(() => {
 		const req = captureNowRequest.data;
 		if (req && hasCamera && !processedCaptureNowIds.has(req._id)) {
@@ -611,6 +644,13 @@
 			{#if draftPhotos.length > 0}
 				<DraftBadge photos={draftPhotos} onremove={handleRemoveDraftPhoto} />
 			{/if}
+			{#if incomingSheetItems.length > 0}
+				<IncomingSheetsPanel
+					sheets={incomingSheetItems}
+					onaccept={handleAcceptSheet}
+					ondismiss={handleDismissSheet}
+				/>
+			{/if}
 			<ChatInput onsubmit={sendMessage} allowEmpty={draftPhotos.length > 0} />
 		</div>
 	{/if}