I'm not sure it's possible to get Assistant voice typing activated - I tried but was not successful.
If you follow "Learn more" link that is next to the grayed out "Assistant voice typing" switch, it mentions that "you may need to update the Android System Intelligence app" - I read that it needs it in order to work. Also, I interpret "Assistant" typing would depend on Google Assistant. I've tried installing both apps above but the switch to activate "Assistant voice typing" never got enabled.
I've allowed a few days with network permissions enabled for Google Assistant and Android System Intelligence (even though it designed for offline use specifically) to see if they would get some kind of update to "hook" into the Gboard but it never happened. I've removed both since then and gave up on the idea enabling Assistant voice typing as its benefits were marginable at best and, in my opinion, not worth the requirements.