feat: complete auth/profile username migration and runtime safeguards

backend/src/v1/auth/schemas.py

@@ -6,9 +6,9 @@ from pydantic import BaseModel, EmailStr, Field
 
 
 class SignupRequest(BaseModel):
+    username: str = Field(min_length=3, max_length=30)
     email: EmailStr
     password: str = Field(min_length=6)
-    display_name: str | None = None
     redirect_to: str | None = None
 
 
@@ -38,6 +38,13 @@ class AuthTokenResponse(BaseModel):
     user: AuthUser
 
 
+class AuthUserByEmailResponse(BaseModel):
+    id: str
+    email: EmailStr
+    created_at: str
+    email_confirmed_at: str | None = None
+
+
 class SignupPendingResponse(BaseModel):
     status: Literal["pending_verification"] = "pending_verification"
     user: AuthUser