You can use fetch api and the POST method to send data to an api. Since you have not provided how your api works or how the data is to be passed I cannot provide further help, but i can guide you to the correct path.

Read more about fetch api in javascript

(async function () {
    const url = ''; // your api endpoint here
    const res = await fetch(url, { method: 'POST' });
    // res corresponds to the api response;
})();

Since you're using jQuery, you should probably read jQuery post method

This should work. Make sure URL for API and web should be the same else you could get cross site error:

<form id="contactForm" class="w-75 mx-auto" action="http://yourAPI.com">
    <input type="text" class="form-control bg-transparent" placeholder="Name">
    <input type="email" class="form-control bg-transparent my-3" placeholder="E-mail">
    <textarea class="form-control bg-transparent" placeholder="Your Message"></textarea>
    <button type="submit" class="my-3 px-4 py-2 rounded-3">SEND</button>
</form>

<script
  src="https://code.jquery.com/jquery-3.6.0.min.js"
  integrity="sha256-/xUj+3OJU5yExlq6GSYGSHk7tPXikynS7ogEvDej/m4="
  crossorigin="anonymous"></script>

<script>
    $('#contactForm').submit(function (e) {
        e.preventDefault(); // avoid to execute the actual submit of the form.

        
        var form = $(this);
        var url = form.attr('action');
        
        $.ajax({
            type: "POST",
            url: url,
            data: form.serialize(), // serializes the form's elements.
            success: function(data)
            {
                alert(data); // show server response 
            }
        });
    });
</script>

$("#contactForm").submit( async (e) => {
    e.preventDefault();
    const data = {
        name: e.target.elements[0].value,
        email: e.target.elements[1].value,
        message: e.target.elements[2].value,
    }
    const response = await fetch(url, {
        method: 'POST', // *GET, POST, PUT, DELETE, etc.
        mode: 'cors', // no-cors, *cors, same-origin
        credentials: 'same-origin', // include, *same-origin, omit
        headers: {
          'Content-Type': 'application/json'
        },
        redirect: 'follow', // manual, *follow, error
        referrerPolicy: 'no-referrer', // no-referrer, *no-referrer-when- 
       downgrade, origin, origin-when-cross-origin, same-origin, strict- 
       origin, strict-origin-when-cross-origin, unsafe-url
       body: JSON.stringify(data) // body data type must match "Content-Type" header
  });
})