In 2022, I'm able to copy from the drawing app of my choice (TVPaint), and then paste it into a video game sprite editor called Aseprite, and immediately cut it and then paste it into Affinity Designer. There's something that Aseprite does to the clipboard transparency when I 'bounce' it off of Aseprite that makes it compatible with Affinity Designer.
Well, I guess since Aseprite has a puny memory footprint I can just leave it running in the background and bounce stuff off of it.
Modern problems require modern solutions.
So, try out pasting transparent objects from all your image editing programs and see if there are any that CAN paste transparent objects directly into your Affinity programs. Once you find an app that can do this, you can then use it as a "clipboard bouncing app" to tide you over until something less janky can be found.