To join the groups as your page (join as your page FIRST then as yourself – not the other way around)

Select the group that you want to join – then click on “join group” (see screenshot below)

If you are an admin on your page it will bring up the options as displayed on the second screenshot.
Join as your page first then as yourself.

We’ve created the settings on the group in such a way that you can join as your page.