One place I can think of is substrate.dev. We could e.g. ask the maintainers to add a top bar there, highlighting that there is currently an ongoing StackExchange Beta and that users should post their questions here (+ look for existing answers).
What are other sites where we should make people aware of this Beta?
It would be resourceful to see the pop-up window shown on https://substrate.io/ to be shown on all pages of https://docs.substrate.io/ as well. As the docs are where most of the devs go to when trying to learn Substrate. That way, new learners of Substrate know where to ask their questions.