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>

docs/couple-pairing.md

@@ -263,6 +263,55 @@ DELETE delete-relationship
 Both users: Unpaired
 ```
 
+## Invite Funnel (Join Links)
+
+The invite code can also be delivered as a tappable link instead of requiring
+the recipient to type it in manually.
+
+**Link forms:**
+- Universal/App Link: `https://sauci.app/join/{code}` (served by `apps/web`,
+  opens the app directly on a device that has it installed and verified).
+- Custom scheme: `app.sauci://join?code={code}` (used by the web join page's
+  automatic hand-off attempt, and remains supported for any existing client
+  behavior).
+
+**Web fallback (`apps/web/app/join/[code]/page.tsx`):** validates the code
+shape client-side only (8-character alphanumeric; never calls a private API),
+attempts the custom scheme link, and otherwise shows the code with a copy
+button plus App Store / Play Store links. Copying only copies the raw code.
+
+**Association files:** `apps/web/public/.well-known/apple-app-site-association`
+and `apps/web/public/.well-known/assetlinks.json` authorize `sauci.app` to open
+the app for `/join/*`. The Apple Team ID (`BXVPBATDZY`, from
+`apps/mobile/app.json` and `apps/mobile/eas.json`) and bundle/package id
+(`com.sauci.app`) are real values already used elsewhere in the repo. The
+Android release certificate SHA-256 fingerprint in `assetlinks.json` is a
+placeholder (`PLACEHOLDER_ANDROID_RELEASE_SHA256_CERT_FINGERPRINT`) and must
+be replaced with the real release signing certificate fingerprint before
+Android App Links will verify.
+
+**Mobile link handling:** `apps/mobile/app.json` declares
+`associatedDomains: ["applinks:sauci.app"]` (iOS) and an intent filter for
+`https://sauci.app/join/*` (Android), in addition to the existing `app.sauci`
+scheme. `apps/mobile/app/_layout.tsx` parses incoming URLs
+(`src/lib/inviteLink.ts`) and either routes a signed-in, onboarded user
+straight to the pairing screen with the code pre-filled, or stashes the code
+(`src/lib/pendingInviteCode.ts`) for signed-out/mid-onboarding users. The
+stashed code is applied once the user reaches the pairing screen or the app's
+initial route (`apps/mobile/app/index.tsx`) after sign-in/onboarding
+completes.
+
+**Deferred clipboard hand-off:** if an unpaired user opens the pairing screen
+with no code from a link or stash, the app checks the clipboard once per
+session (`src/lib/clipboardInviteOffer.ts`) for a string matching the invite
+code shape and offers to use it ("Use code XXXXXXXX from your clipboard?").
+The code is never applied automatically; the user must accept the offer.
+
+**Analytics:** `invite_link_opened` (`source`: `universal_link` | `scheme` |
+`clipboard`), `pairing_code_prefilled` (mobile, Firebase Analytics), and
+`join_page_viewed` / `join_page_code_copied` / `join_page_store_button_clicked`
+(web, PostHog).
+
 ## Cascade Behavior
 
 When a couple is deleted, foreign key cascades clean up: