Fixed the sweepstakes landing page with new legal rules (#47246)

## I have read the
[CONTRIBUTING.md](https://github.com/supabase/supabase/blob/master/CONTRIBUTING.md)
file.

YES

## What kind of change does this PR introduce?

Added alternative means of entry forms and added a new email for legal
contest inquiries.

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->

## Summary by CodeRabbit

* **Updates**
* Updated the contact email for the contest winners list request in the
contest rules page, improving accessibility.
* Enhanced the legal/amoe form with integrated customer data management
capabilities for more efficient form submission and data handling.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

apps/www/_go/legal/amoe.tsx

@@ -62,6 +62,15 @@ const page: GoPageInput = {
             company_name: 'company_name',
           },
         },
+        notion: {
+          database_id: '3885004b775f80b98198f7497946e54d',
+          columnMap: {
+            first_name: 'First Name',
+            last_name: 'Last Name',
+            email_address: 'Email',
+            company_name: 'Company',
+          },
+        },
       },
     },
   ],

apps/www/_go/legal/contest-rules.tsx

@@ -137,10 +137,12 @@ const page: GoPageInput = {
 
   For a copy of the winners list, send a request to:
 
-  [legal@supabase.com](mailto:legal@supabase.com)
+  [sweepstakes@supabase.com](mailto:sweepstakes@supabase.com)
 
   within sixty (60) days of the end of the Promotion.
 
+  To enter without purchase, use the [Alternative Mode of Entry](/go/legal/amoe).
+
   © 2026 Supabase Inc.
 
   [Privacy Policy](https://supabase.com/privacy) · [Terms of Service](https://supabase.com/terms) · [Alternative Mode of Entry](/go/legal/amoe)