Make invite code optional in frontend when backend allows it

- Remove required attribute from invite code field
- Only validate invite code if one is entered
- Only include invite_code in request if provided

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

frontend/src/pages/RegisterPage.tsx

@@ -40,12 +40,8 @@ export function RegisterPage() {
     setLocalError('')
     clearError()
 
-    if (!inviteCode.trim()) {
-      setLocalError('Invite code is required')
-      return
-    }
-
-    if (inviteCodeStatus !== 'valid') {
+    // Only validate invite code if one was entered
+    if (inviteCode.trim() && inviteCodeStatus === 'invalid') {
       setLocalError('Please enter a valid invite code')
       return
     }
@@ -66,7 +62,11 @@ export function RegisterPage() {
     }
 
     try {
-      await register({ email, password, name, invite_code: inviteCode.trim() })
+      // Only include invite_code if provided
+      const userData = inviteCode.trim()
+        ? { email, password, name, invite_code: inviteCode.trim() }
+        : { email, password, name }
+      await register(userData)
       navigate('/trees', { replace: true })
     } catch {
       // Error is set in the store
@@ -97,7 +97,6 @@ export function RegisterPage() {
                 id="inviteCode"
                 name="inviteCode"
                 type="text"
-                required
                 value={inviteCode}
                 onChange={(e) => {
                   setInviteCode(e.target.value.toUpperCase())