After quite some tinkering, it turns out that terminus doesn't change the cursor shape in my iTerm2 with Tmux.
I found that the right setup was using the standard terminal option and commenting out the tmux specific update:

I'm running TERM_PROGRAM_VERSION=3.3a
I don't know why that could be the case, I'm not super knowledgeable about that but if someone has the same issue at least they can find a workaround.