Why is form submission (register) not launching from my vuejs application ? Nothing in console

Thank you for your help.
I work on an application, I have to manage the frontend part with vue.js and the backend part with express.js, mysql.

One important thing I currently only work on requests in VueJS: Fetch API.
When I restart the front part and do a simulation nothing is displayed on my console.
I declared my data, method, fetch API.

-Authentication with Vue 3 : Registration and login.
-The page in question is the registration.
I then go to the backend to do the controllers, route, auth part, for secure authentication on mysql.

<script>
export default {
  name: "FormSuscribe",

  data() {
    return {
      first_name: "",
      email: "",
      password_key: "",
    };
  },

  methods: {
    signup() {
      fetch("http://localhost:3000/api/auth/signup", {
        method: "POST",
        //--Header--//
        headers: {
          Authorization: "Bearer ",
          Accept: "application/json",
          "Content-Type": "application/json",
        },
        //---Body--//
        body: JSON.stringify({
          name: this.name,
          email: this.email,
          password: this.password,
        }),
      });
    },
  },
};
</script>
<template>
  <main>
    <section class="form my-4 mx-5">
      <div class="container">
        <div class="row">
          <div class="col-lg-5 g-0">
            <img
              src="@/assets/signup-image.jpg"
              class="img-fluid first-img"
              alt="Office"
            />
          </div>
          <div class="col-lg-7 px-5 pt-5">
         

            <form method="post" @submit="signup">
              <div class="form-row">
                <div class="col">
                  <input
                    id="first_name"
                    name="username"
                    placeholder="Nom"
                    class="my-3 p-2"
                    v-model="first_name"
                  />
                </div>
              </div>
              <div class="form-row">
                <div class="col">
                  <input
                    type="email"
                    id="email"
                    name="email"
                    class="form-group my-3 p-2"
                    placeholder="[email protected]"
                    v-model="email"
                  />
                </div>
              </div>

              <div class="form-row">
                <div class="col">
                  <input
                    type="password"
                    id="password"
                    name="password"
                    placeholder="**********"
                    class="my-3 p-2"
                    v-model="password_key"
                  />
                </div>
              </div>

              <div class="form-row">
                <div class="col-lg-4">
                  <button type="button" class="btn fw-bold">register</button>
                  <a href="">Forgot password</a>
                  <p>
                    You already have an account <a href="#">Connect</a>
                  </p>
                </div>
              </div>
            </form>
          </div>
        </div>
      </div>
    </section>

    <div class="container text-center">
      <img
        src="@/assets/icon-left-font-black.webp"
        class="img-fluid col-lg-2 col-sm-2"
        alt="Brand "
      />
    </div>
  </main>
</template>