fix(api): propagate requestId for register and reset-password

Backend requires X-Request-Id header from the verification code send
response. Wire requestId through email/auth-extra API returns, register
and forgot-password pages, and auth API request headers.

lib/api/email.ts

@@ -1,11 +1,18 @@
 import { httpJson } from "./http"
 
+interface SendVerificationCodeResp {
+  requestId: string
+  expireInSec: number
+  message: string
+}
+
 export async function sendEmailVerificationCode(input: {
   email: string
   scene: string
-}): Promise<void> {
-  await httpJson<unknown>("/api/v1/email/verification-code/send", {
+}): Promise<string> {
+  const res = await httpJson<SendVerificationCodeResp>("/api/v1/email/verification-code/send", {
     method: "POST",
     json: { email: input.email, scene: input.scene },
   })
+  return res.requestId
 }