Last year, when I suddenly had to teach symbol-heavy stuff over the internet, I put together a tool for this because my handwriting is just too bad with a mouse or even a tablet. I wanted to be able to "live" calculate with symbols while I talked over it with my students.
I called this tool √𝚎𝚍, the rich Unicode text editing suite (RUTED, pronounced ˈruːtɪd) and I use it in vim: https://gitlab.com/ruted/ruted-vim.
I first defined so called modes of ASCII sequences representing Unicode symbols, like "forall" for "∀", and "NN" for "ℕ", and ";o" for "∘". Then I created a very small vim plugin to enable modes and change modes. When in a mode, you can enter the ASCII sequences, and they are replaced by their Unicode equivalent.
It is a bit of a simple hack, but it worked great over the past year. Entering symbols has become very easy for me now.