With that I mean UI elements (for example text fields and animated buttons) that are not restricted to the monospaced character grid of terminal emulators, but can be arbitrary shapes at arbitrary pixel positions on the screen. I’m simply curious whether and how that is possible, and if it’s not possible, whether it’s planned for the future.
Textfields and buttons (like, in the Customize buffers) are actually subject to the grid Emacs aligns characters on.
What you can do is telling Emacs to display an image of the SVG (vector) or XPM (bitmap) type. Since those aren't limited to be read in from a file, you can generate a string and turn it into an image. I've seen examples of both canvas-like usage where the image occupies most of the window and is freely drawn on (see svg-thing, slime-volley, svg-clock, my own svg-2048) and less obnoxious usage which rather resemble UI elements (see the icons in AUCTEX, gnus' modeline icon, the graphical version of
M-x tetris, svg-modeline). There's still quite a bit of footwork to do considering Emacs does not have a canvas-like image type, but it's possible to displace these images and to use them as display property of other UI elements like the modeline or margin and bind keys including the mouse ones to them.
For drawing raster graphics you might try EPaint. It appears to support freehand drawing and basic geometric shapes.