This should be how to do it:
Please note the notification at the top of the article:
"If you can't join a group as your Facebook Page, it might be because the group admins don't allow Pages to join their groups."
This means that if one of the local community groups (if not all) don't allow pages to join, you actually can't do it at all. The only solution then is to ask the community if they will allow it.
For classic pages where you're already joined as a profile/person this should be the way to do it:
- Go to that particular group and leave with your profile.
- Join again as a page.
- Visit the group and under the timeline, you should see the "interact as" menu.
- Then you click on your profile and reload the group
You should see that you have to join it again as your profile.
If this does not work, the group simply does not allow pages to join. Which can still be the case as pointed out by the Facebook documentation:
"Group admins might not allow Pages to join their groups.