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/auth-extra.ts

@@ -1,8 +1,15 @@
 import { httpJson } from "./http"
 
-export async function sendForgotPasswordCode(email: string): Promise<void> {
-  await httpJson<unknown>("/api/v1/auth/forgot-password/send", {
+interface SendVerificationCodeResp {
+  requestId: string
+  expireInSec: number
+  message: string
+}
+
+export async function sendForgotPasswordCode(email: string): Promise<string> {
+  const res = await httpJson<SendVerificationCodeResp>("/api/v1/auth/forgot-password/send", {
     method: "POST",
     json: { email },
   })
+  return res.requestId
 }