If you take a look at a standard TButton on Windows 7 and above, hovering the mouse over the button will produce a subtle fade in effect, while taking the cursor away will make the hot face of the button fade out quickly.
If you check the same with a TBitBtn you'll see that there's no fade effect; it changes to the hot state without any transition then changes back without any transition too.
Is there any component similar to TBitBtn that can display a picture and that is properly themed at the same time?
Yes, you can use TButton which is a native Windows BUTTON control, and it does support icons via an image list. But beware of the bug!