david-rui/slick ? reverse-engineered prompt

Build me a slick carousel plugin for jQuery that I can drop into a website and use on almost any kind of content.

I want it to let me make sliders with next and previous arrows, dots, autoplay, infinite looping, touch and mouse dragging, responsive breakpoints, lazy loading, and options for things like showing multiple slides, fading between slides, vertical mode, centered slides, and syncing one slider to another. It should work nicely on mobile and desktop, and I should be able to configure it with normal JavaScript or with data attributes on the element.

Please include the basic CSS for the default look, a themed style, and a simple demo page that shows the main features working. Make sure it is compatible with jQuery 4, and if you need to check anything current, look up the latest docs online.