This is how you can make datepicker in React with react-datepicker and style this in Tailwind.
By the time of making this, datepicker for Headless UI didn't exist, and there were no docs on any popular react datepicker library about how to make it work with Tailwind.
As a result I spent fuckton of time inspecting classes in Chrome devtools and styling them in Tailwind manually. I think I made a decent job and hope it saves someone some time.
This is not a package, just some code for you to get idea how to do it in your project.