I think using herd immunity to apply to temporary network states is going to be more confusing than helpful. There will be some fuzziness at the edges - some of the changes and adaptations we make during this pandemic will probably persist longer term.

R₀ is used to describe that (roughly anyway, I think it doesn't align exactly with what you are saying).

Herd immunity means that enough people are immune to drive R₀ below 1, absent other factors. So the number of infections would decrease without social distancing and without mask wearing and so on.

The reason herd immunity gets so much attention is because it is the threshold where things can go back to normal. If you redefine it to include mitigations, then you need another term for when you can reasonably safely cease those mitigations.

(Hopefully we can get herd immunity with a safe vaccine, rather than the majority of the population getting infected)