I have an input on my webpage that I am able to set the date on by getting an ISO string and pulling out the first 10 characters.
date = new Date();
dateInpu         
        
Try using .toLocaleString to get the date into the input, and add the time when parsing it, like this:
date = new Date();
dateInput.value = date.toLocaleString("sv-SE", {
    hour: "2-digit",
    minute: "2-digit",
    second: "2-digit"
});
And to get the value into a Date object use:
new Date(inputdateInput.value + "T00:00");
I wrote a little post about converting between Date objects and date inputs here