[Vuejs]-Why vue.js component is not set the Data from method

You don’t have access to this in your .then callback. So you’re trying to assign something to users on undefined.
This article explains the reason why.
Try changing your promise callback to use an arrow function, such as:

userRequests: function() {
  axios.post('/api/user_requests')
  .then(response => {
    console.log(response.data)
        this.users = response.data.data;
    })
    .catch(function (error) {
        console.log(error);
    }) 
}

Try this way

export default {
  name: "videoChat",
  data() {
    return {
      users: [],
    };
  },
  methods: {
    async userRequests() {
      try {
        const { data } = await axios.post(`/api/user_requests`);
        this.users = data;
      } catch (error) {
          console.log('error', error)
      }
    },
  },
  mounted() {
    this.userRequests();
  },
};

Assign to users[] just response.data and not response.data.data . Here you have a functional example:
https://codepen.io/jssDev-/pen/zYEExbq

If you don’t want to use arrow function, you can also save this reference and use it later in the function. Make sure to do this before the axios call.

userRequests: function() {
  let vm = this
  axios.post(`/api/user_requests`).then(function (response) {
    vm.users = response.data.data
  }).catch(function (error) {
    console.log(error)
  }) 
},