fix(www): correct feature statuses, MCP Server copy, and self-hosted flags (#43223)

## 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?

A content/data fix: correcting stale feature metadata on the marketing
features page and docs feature status table.

## What is the current behavior?

Several features in features.tsx (supabase.com/features) have incorrect
stage or self-hosted availability values that are out of sync with docs.

## What is the new behavior?

branching
- stage updated to Beta

vault
- stage updated to Public Alpha

jwt-signing-keys
- availableOnSelfHosted set to true

persistent-storage
- docs URL corrected to /guides/functions/ephemeral-storage
- env var names corrected to S3FS_ACCESS_KEY_ID, S3FS_SECRET_ACCESS_KEY,
S3FS_REGION, S3FS_ENDPOINT_URL

features.mdx
- PrivateLink row added to the Platform section (beta, N/A for
self-hosted)

mcp-server
- removed "upcoming" from OAuth benefit (OAuth is now live), updated PAT
FAQ (OAuth is now default, PAT only needed for CI/CD), updated
self-hosted FAQ (self-hosted is supported via
/guides/self-hosting/enable-mcp)

## Additional context

N/A

---------

Co-authored-by: Ana Mogul <ana1337x@users.noreply.github.com>

apps/docs/content/guides/getting-started/features.mdx

@@ -218,6 +218,7 @@ In addition to the Beta requirements, features in GA are covered by the [uptime
 | Platform       | Read Replicas              | `GA`            | N/A                                         |
 | Platform       | Log Drains                 | `public alpha`  | ✅                                          |
 | Platform       | MCP                        | `public alpha`  | ✅                                          |
+| Platform       | PrivateLink                | `beta`          | N/A                                         |
 | Studio         |                            | `GA`            | ✅                                          |
 | Studio         | SSO                        | `GA`            | ✅                                          |
 | Studio         | Column Privileges          | `public alpha`  | ✅                                          |

apps/www/data/features.tsx

@@ -413,7 +413,7 @@ Supabase Branching allows you to create and test changes in separate, temporary
     docsUrl: 'https://supabase.com/docs/guides/platform/branching',
     slug: 'branching',
     status: {
-      stage: PRODUCT_STAGES.GA,
+      stage: PRODUCT_STAGES.BETA,
       availableOnSelfHosted: false,
     },
   },
@@ -683,7 +683,7 @@ This feature is particularly useful for teams looking to enhance their security
     docsUrl: 'https://supabase.com/docs/guides/database/vault',
     slug: 'vault',
     status: {
-      stage: PRODUCT_STAGES.PUBLIC_BETA,
+      stage: PRODUCT_STAGES.PUBLIC_ALPHA,
       availableOnSelfHosted: true,
     },
   },
@@ -1236,7 +1236,7 @@ JWT Signing Keys provide modern, secure JWT management with the flexibility requ
     slug: 'jwt-signing-keys',
     status: {
       stage: PRODUCT_STAGES.GA,
-      availableOnSelfHosted: false,
+      availableOnSelfHosted: true,
     },
   },
   {
@@ -1946,13 +1946,13 @@ Persistent Storage backed by S3 protocol survives invocations. Ephemeral Storage
 - Machine learning model storage
 
 ## Setup
-Requires S3 credentials as environment variables: \`AWS_ACCESS_KEY_ID\`, \`AWS_SECRET_ACCESS_KEY\`, \`AWS_REGION\`, \`AWS_ENDPOINT_URL_S3\`.
+Requires S3 credentials as environment variables: \`S3FS_ACCESS_KEY_ID\`, \`S3FS_SECRET_ACCESS_KEY\`, \`S3FS_REGION\`, \`S3FS_ENDPOINT_URL\`.
 
 Persistent Storage transforms Edge Functions into stateful, high-performance computing environments.`,
     icon: UploadCloud,
     products: [PRODUCT_SHORTNAMES.FUNCTIONS],
     heroImage: '',
-    docsUrl: 'https://supabase.com/docs/guides/storage',
+    docsUrl: 'https://supabase.com/docs/guides/functions/ephemeral-storage',
     slug: 'persistent-storage',
     status: {
       stage: PRODUCT_STAGES.GA,
@@ -2881,7 +2881,7 @@ The MCP Server simplifies the integration of AI tools with Supabase, enabling a
 2. Standardized tool ecosystem: MCP standardizes how tools interact with Supabase, enabling a plug-and-play experience for AI-powered workflows.
 3. Streamlined workflows: Build faster by offloading repetitive tasks like schema design and configuration management to your AI assistant.
 4. Extensive toolset: Access over 20 tools for database design, data querying, and project management.
-5. Evolving capabilities: MCP continues to evolve, with upcoming support for native OAuth authentication, Edge Function deployment, and advanced schema discovery.
+5. Evolving capabilities: MCP continues to evolve, with support for native OAuth authentication, Edge Function deployment, and advanced schema discovery.
 
 The MCP Server empowers developers to build AI-native applications, accelerating productivity and reducing the complexity of working across multiple tools.
 
@@ -2916,11 +2916,11 @@ MCP is a standard that defines how AI tools and platforms communicate. It enable
 
 ### Do I need a personal access token (PAT) to use the MCP Server?
 
-Yes, you'll need to create a PAT in your Supabase settings to authenticate the MCP Server. Future versions of MCP will support OAuth login flows for simpler authentication.
+No, a PAT is no longer required. The MCP Server now uses OAuth by default via dynamic client registration, so your AI tool authenticates through a browser-based flow. A PAT is only needed for CI/CD or non-interactive scenarios.
 
 ### Can I use the MCP Server with self-hosted Supabase instances?
 
-No, the official Supabase MCP Server connects directly to Supabase Cloud. For local instances, you can use the Postgres MCP Server instead.
+Yes, self-hosted Supabase instances are supported. Follow the [self-hosted MCP guide](/docs/guides/self-hosting/enable-mcp) to configure secure access via SSH tunnel or VPN.
 
 ### Which AI tools are compatible with the MCP Server?