feat(invites): wire EmailService.send_account_invite_email into create handler

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

backend/app/api/endpoints/accounts.py

@@ -260,7 +260,7 @@ async def create_invite(
     db: Annotated[AsyncSession, Depends(get_db)],
     current_user: Annotated[User, Depends(require_account_owner)]
 ):
-    """Create an invite to join this account (owner only)."""
+    """Create an invite to join this account (owner only). Sends invite email."""
     code = secrets.token_urlsafe(16)
 
     expires_at = None
@@ -276,6 +276,24 @@ async def create_invite(
         expires_at=expires_at,
     )
     db.add(invite)
+    await db.flush()
+
+    # Lookup account name for email
+    account_result = await db.execute(
+        select(Account).where(Account.id == current_user.account_id)
+    )
+    account = account_result.scalar_one()
+
+    # Send invite email — non-blocking on failure (function returns False on error)
+    email_sent = await EmailService.send_account_invite_email(
+        to_email=invite.email,
+        code=code,
+        account_name=account.name,
+        role=invite.role,
+    )
+    if email_sent:
+        invite.email_sent_at = datetime.now(timezone.utc)
+
     await db.commit()
     await db.refresh(invite)
     return invite