I haven't checked out starship yet, but if I understand what you are using, that is Zle functionality. It's part of OMZs configuration (here: https://github.com/ohmyzsh/ohmyzsh/blob/master/lib/key-bindi...) but doesn't use other OMZ features.

I don't know if starship is still using Zle. If so, this should be possible to configure without OMZ.