I found that using script to preserve colors when piping to less doesn't really work (less is all messed up and on exit, bash is all messed up) because less is interactive. script seems to really mess up input coming from stdin even after exiting.
So instead of running:
script -q /dev/null cargo build | less -R
I redirect /dev/null to it before piping to less:
script -q /dev/null cargo build < /dev/null | less -R
So now script doesn't mess with stdin and gets me exactly what I want. It's the equivalent of command | less but it preserves colors while also continuing to read new content appended to the file (other methods I tried wouldn't do that).