How to set cookies for Next.js application from a separate server?

Question

Node.js

I have a server application separate from Next.js on NeSt, which implements all the business logic. When trying to log in to the Next.js application, there is a problem that cookies from NeSt are not set in the browser. When working with postman cookies are set.
How cookies are set: (/auth/sign-in)

async login(@Req() req: IReq, @Res() res: Response<string>): Promise<void> {
    const tokens = await this.authService.createTokens(req.user);
    
    res.cookie("refresh_token", tokens.refresh_token, {
      httpOnly: true,
      maxAge: 1000 * 60 * 60 * 24 * 30,
      signed: true
    });

    res.json(tokens.access_token).status(201);
  }

Server request:

export async function login(data: any) {
  const headers = new Headers();
  headers.set("Content-Type", "application/x-www-form-urlencoded");

  const response = await fetch(`${process.env.API_URL}/auth/sign-in`, {
    method: "POST",
    headers,
    body: new URLSearchParams({ ...data, username: data.email })
  });

  if (response.ok) {
    return null;
    return {
      access_token: await response.json()
    };
  } else {
    return null;
  }
}

When checking cookies in the browser, there is nothing there.