This has less to do with distro, and more to do with Desktop Environment choice. Anything on Wayland is great with touchscreens. I’m on Plasma, and it’s pretty fantastic.
No, you’ve got it set up right. Many people will have graphs where each character rectangle has open circles for the unused braile dots in the character block.
Pro tip: configure a font that doesn’t show open circles for unused braille characters to have a higher priority than your current font to get better-looking graphs.
On my system, braille characters are provided by DejaVu Serif, and it was as easy as just installing the font.