That sleeve is called a quill and it has its own oversized ID release bearing (they come together as a kit). The quill has locktite on it, so it doesn't just slide off. The quill and oversized ID release bearing is so common now, that it is almost the new standard. Unless your standard release bearing is new, I would replace it, as that is what fails first. Shop around for a new release bearing. The Ceramic release bearing is only $50.00 or so, so the standard one should be very economical.
There is a small chance your new tranny has wear on that input shaft and that is why the quill is there. I believe the quill is hardened steel while the original input shaft surface is softer carbon steel.... thus the wear.