How do I add a search field to a social network clone?

Question

firebase

I want to add to my clone the ability to search for other registered people, like in social networks, enter "Eli" for example, and it shows all users whose first / last name begins with these letters, or displays in full if you write completely.

Registered users are in the Realtime database in firebase (naturally, email / password registration is enabled.) Below is a screen.


How can I make this possible now?

Here is the component from which I need to make a "search engine"

<template>
  <div class="search">
    <input type="search" placeholder="Search Twitter" v-model="search" />
  </div>
</template>

<script>
export default {
  data() {
    return {
      search: "",
    };
  },
  methods: {

  },
};
</script>