feat(invite-funnel): add web join page and mobile deep-link hand-off

Adds a shareable https://sauci.app/join/{code} link as an alternative to
manually typing an 8-character invite code:

- apps/web: /join/[code] page that validates the code shape client-side,
  attempts the app.sauci:// scheme link, and falls back to a large code
  display with copy button plus App Store/Play Store links; PostHog events
  for page view, code copy, and store-button clicks.
- apps/web: apple-app-site-association and assetlinks.json under
  /.well-known so iOS Universal Links and Android App Links can verify
  sauci.app for /join/*. The Android release cert SHA-256 fingerprint is a
  placeholder pending the real value.
- apps/mobile: associated domains (iOS) and an intent filter (Android) for
  https://sauci.app/join/*, alongside the existing app.sauci scheme.
- apps/mobile: parse incoming join links, pre-fill and highlight the code on
  the pairing screen, stash the code for signed-out/mid-onboarding users and
  apply it once they reach pairing, and offer a once-per-session clipboard
  hand-off that is never auto-applied.
- apps/mobile: share message now leads with the join link, keeping the raw
  code visible as a fallback.
- Analytics: invite_link_opened, pairing_code_prefilled (mobile);
  join_page_viewed, join_page_code_copied, join_page_store_button_clicked
  (web).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

apps/mobile/src/lib/analytics.ts

@@ -272,6 +272,9 @@ export const Events = {
 
   // Invite events
   inviteCodeCopied: () => logEvent("invite_code_copied"),
+  inviteLinkOpened: (source: "universal_link" | "scheme" | "clipboard") =>
+    logEvent("invite_link_opened", { source }),
+  pairingCodePrefilled: () => logEvent("pairing_code_prefilled"),
 
   // Tutorial events
   tutorialStarted: (tutorial: "swipe" | "matches") =>

apps/mobile/src/lib/clipboardInviteOffer.ts

@@ -0,0 +1,39 @@
+// Deferred hand-off fallback: when a user copies an invite code on another
+// device (e.g. from the web join page) then opens the app, offer to use the
+// code found on the clipboard. Never auto-applies the code; the caller must
+// present a confirmation before using the result. Only checks once per app
+// session so the user is not repeatedly prompted.
+
+import * as Clipboard from "expo-clipboard";
+import { isValidInviteCode, normalizeInviteCode } from "./inviteLink";
+
+let hasCheckedThisSession = false;
+
+/**
+ * Checks the clipboard once per session for a string matching the invite
+ * code shape. Returns the normalized code, or null when there is nothing
+ * usable (or the check already ran this session).
+ */
+export async function checkClipboardForInviteCode(): Promise<string | null> {
+    if (hasCheckedThisSession) return null;
+    hasCheckedThisSession = true;
+
+    try {
+        const hasString = await Clipboard.hasStringAsync();
+        if (!hasString) return null;
+
+        const value = await Clipboard.getStringAsync();
+        if (value && isValidInviteCode(value)) {
+            return normalizeInviteCode(value);
+        }
+    } catch (error) {
+        console.error("Error checking clipboard for invite code:", error);
+    }
+
+    return null;
+}
+
+/** Test-only helper to reset the per-session gating between test cases. */
+export function __resetClipboardInviteOfferForTests(): void {
+    hasCheckedThisSession = false;
+}

apps/mobile/src/lib/inviteLink.ts

@@ -0,0 +1,76 @@
+// Shared invite code shape and deep-link parsing for the invite funnel.
+//
+// Two link forms carry an invite code into the app:
+//   - Universal/App Link: https://sauci.app/join/{code}
+//   - Custom scheme link: app.sauci://join?code={code}
+//
+// Both forms are handled by the root layout's deep link listener and by the
+// pairing screen when it receives a `code` route param.
+
+export const INVITE_CODE_LENGTH = 8;
+const INVITE_CODE_PATTERN = /^[A-Z0-9]{8}$/;
+
+export type InviteLinkSource = "universal_link" | "scheme";
+
+export interface ParsedInviteLink {
+    code: string;
+    source: InviteLinkSource;
+}
+
+/**
+ * Returns true when `code` (case-insensitive) matches the 8-character
+ * alphanumeric invite code shape used across the app.
+ */
+export function isValidInviteCode(code: string | null | undefined): boolean {
+    if (!code) return false;
+    return INVITE_CODE_PATTERN.test(code.trim().toUpperCase());
+}
+
+/**
+ * Normalizes a raw invite code string to the canonical uppercase form used
+ * for display, storage, and API calls.
+ */
+export function normalizeInviteCode(code: string): string {
+    return code.trim().toUpperCase();
+}
+
+/**
+ * Parses an incoming URL for an invite code, supporting both the universal
+ * link form (https://sauci.app/join/{code}) and the custom scheme form
+ * (app.sauci://join?code={code}). Returns null when the URL does not carry a
+ * recognizable, validly-shaped invite code.
+ */
+export function parseInviteLinkCode(url: string | null | undefined): ParsedInviteLink | null {
+    if (!url) return null;
+
+    let parsed: URL;
+    try {
+        parsed = new URL(url);
+    } catch {
+        return null;
+    }
+
+    let rawCode: string | null = null;
+    let source: InviteLinkSource | null = null;
+
+    if (parsed.protocol === "https:" && parsed.hostname === "sauci.app") {
+        const match = parsed.pathname.match(/^\/join\/([^/]+)\/?$/);
+        if (match) {
+            rawCode = match[1];
+            source = "universal_link";
+        }
+    } else if (parsed.protocol === "app.sauci:") {
+        const host = parsed.hostname || parsed.pathname.replace(/^\/+/, "");
+        if (host === "join") {
+            rawCode = parsed.searchParams.get("code");
+            source = "scheme";
+        }
+    }
+
+    if (!rawCode || !source) return null;
+
+    const code = normalizeInviteCode(rawCode);
+    if (!isValidInviteCode(code)) return null;
+
+    return { code, source };
+}

apps/mobile/src/lib/pendingInviteCode.ts

@@ -0,0 +1,37 @@
+// Deferred hand-off storage for an invite code received before the user is
+// signed in or has finished onboarding. The code is applied once the user
+// reaches the pairing screen (see app/(app)/pairing.tsx and app/index.tsx).
+
+import AsyncStorage from "@react-native-async-storage/async-storage";
+import { isValidInviteCode, normalizeInviteCode } from "./inviteLink";
+
+const STORAGE_KEY = "pending_invite_code";
+
+export async function stashPendingInviteCode(code: string): Promise<void> {
+    try {
+        await AsyncStorage.setItem(STORAGE_KEY, normalizeInviteCode(code));
+    } catch (error) {
+        console.error("Error stashing pending invite code:", error);
+    }
+}
+
+export async function getPendingInviteCode(): Promise<string | null> {
+    try {
+        const value = await AsyncStorage.getItem(STORAGE_KEY);
+        if (value && isValidInviteCode(value)) {
+            return normalizeInviteCode(value);
+        }
+        return null;
+    } catch (error) {
+        console.error("Error reading pending invite code:", error);
+        return null;
+    }
+}
+
+export async function clearPendingInviteCode(): Promise<void> {
+    try {
+        await AsyncStorage.removeItem(STORAGE_KEY);
+    } catch (error) {
+        console.error("Error clearing pending invite code:", error);
+    }
+}