JSFiddle - React, Tailwind, and code Playground

HTML

<form action="#" method="post" class="" id="form">
    <input type="text" id="todaysDate" name="todaysDate" value="" />
    <input type="button" id="setDate" value="Today"></input>    
</form>

JavaScript

function setDate() {

    var now = new Date(); 
    var day = ("0" + now.getDate()).slice(-2);
    var month = ("0" + (now.getMonth() + 1)).slice(-2);
    var today = now.getFullYear()+"-"+(month)+"-"+(day) ;
    
    $('#todaysDate').val(today);
    
}

$('#setDate').click(function(){
    
    setDate();
    
});