spec: regenerate api-surface-declarations and identity reference docs

Claude-Session: https://claude.ai/code/session_019srGWGCBBCBHqcDoRZpQRh
Co-authored-by: Claude <noreply@anthropic.com>

Author: claude

content/docs/references/identity/organization.mdx

@@ -42,7 +42,7 @@ const result = InvitationSchema.parse(data);
 | **expiresAt** | `string` | ✅ | Invitation expiry timestamp |
 | **inviterId** | `string` | ✅ | User ID of the inviter |
 | **createdAt** | `string` | ✅ | Invitation creation timestamp |
-| **updatedAt** | `string` | ✅ | Last update timestamp |
+| **updatedAt** | `string` | optional | Last update timestamp (no such column on sys_invitation; absent on the wire) |
 
 
 ---
@@ -71,7 +71,7 @@ const result = InvitationSchema.parse(data);
 | **userId** | `string` | ✅ | User ID |
 | **role** | `string` | ✅ | Member role (owner, admin, delegated_admin, member — ADR-0108 closed vocabulary) |
 | **createdAt** | `string` | ✅ | Member creation timestamp |
-| **updatedAt** | `string` | ✅ | Last update timestamp |
+| **updatedAt** | `string` | optional | Last update timestamp (no such column on sys_member; absent on the wire) |
 
 
 ---
@@ -88,7 +88,7 @@ const result = InvitationSchema.parse(data);
 | **logo** | `string \| null` | optional | Organization logo URL |
 | **metadata** | `Record<string, any>` | optional | Custom metadata |
 | **createdAt** | `string` | ✅ | Organization creation timestamp |
-| **updatedAt** | `string` | ✅ | Last update timestamp |
+| **updatedAt** | `string` | optional | Last update timestamp (absent on the better-auth organization wire) |
 
 
 ---

packages/spec/api-surface-declarations/identity.txt

@@ -256,7 +256,7 @@ declare const InvitationSchema: z.ZodObject<{
     expiresAt: z.ZodString;
     inviterId: z.ZodString;
     createdAt: z.ZodString;
-    updatedAt: z.ZodString;
+    updatedAt: z.ZodOptional<z.ZodString>;
 }, z.core.$strip>;
 
 // ── InvitationStatus (const) ──
@@ -293,7 +293,7 @@ declare const MemberSchema: z.ZodObject<{
     userId: z.ZodString;
     role: z.ZodString;
     createdAt: z.ZodString;
-    updatedAt: z.ZodString;
+    updatedAt: z.ZodOptional<z.ZodString>;
 }, z.core.$strip>;
 
 // ── ORGANIZATION_ADMIN (const) ──
@@ -316,7 +316,7 @@ declare const OrganizationSchema: z.ZodObject<{
     logo: z.ZodOptional<z.ZodNullable<z.ZodString>>;
     metadata: z.ZodOptional<z.ZodRecord<z.ZodString, z.ZodUnknown>>;
     createdAt: z.ZodString;
-    updatedAt: z.ZodString;
+    updatedAt: z.ZodOptional<z.ZodString>;
 }, z.core.$strip>;
 
 // ── Position (type) ──