JSFiddle - React, Tailwind, and code Playground

HTML

<!-- html ng-app="app" -->

<!--header-->
<script type="text/javascript" src="js/angular.min.js"></script>
<script type="text/javascript" src="js/app.js"></script>

<!--body ng-controller="AJAXController as ajax" -->
  <label class="appointment-block__label" for="appointment-block__inputs-name">Ваше имя</label>
  <br>
  <input ng-model="ajax.data.name" class="appointment-block__input appointment-block__name" id="appointment-block__inputs-name" type="text" autocomplete="on" required>
  <br>
  <label class="appointment-block__label" for="appointment-block__inputs-tel">Номер телефона</label>
  <br>
  <input ng-model="ajax.data.phone" class="appointment-block__input appointment-block__tel" id="appointment-block__inputs-tel"type="tel" autocomplete="tel" required>
  <br>
  <input ng-click="ajax.send_ajax('php/ajax.php')" class="btn btn-cta appointment-block__input" id="appointment-block__inputs-submit" type="button" value="Записаться на бесплатный приём">
  
  <div>
    {{ say_what }}
  </div>

<!-- /html -->

JavaScript

// js/app.js

(function() {
    var app = angular.module("app", []);

    app.controller("AJAXController", ["$scope", "$http", function($scope, $http) {
        this.data = {};

        // the name of your index in POST array will be A FUCKING STRING like "{name: bla, tel: 123}",
        // so don't forget to decode data in php file like $angular_post = json_decode(file_get_contents('php://input'));
        this.send_ajax = function(url) {
            $http({
                method: "post",
                url: url,
                data: this.data
            }).then(function(response) {
                $scope.say_what = response.data;
            });
        }

    }]);

})();