Hi John,
- “The problem I'm having now is when I try to create public folder subfolders in Outlook or exchange online”
OWA (Outlook Web App) is supported, but with limitations. You can add and remove favorite public folders and perform item-level operations such as creating, editing, deleting posts, and replying to posts.
However, you can’t create or delete public folders from Outlook Web App.
2. “they display as root folders in Outlook. And in the right-click menu, New Folder, Rename Folder, Move folder, Delete and Delete All are greyed out.”
After creating a public folder mailbox, you can create a public folder in EAC (Exchange admin center) and enable mail settings, assigning permission to users.
By default, this folder will be the root folder. If we want to use the public folder in OWA, please right-click
Favorites > Add public folder to Favorites.
For Outlook client, please choose folder navigation and expand All Public Folders under your primary mailbox folder. In the right-click menu, you can only choose
New folder, Copy folder or Add to Favoritesoption**.**

if you want to create a subfolder, just click New folder > input name and Select where to place the folder >OK
Right-clicking the subfolder, you can do any action within your permission.
Note: some actions may not take effect immediately.
Moreover, I think these articles below may help you.
- Public folders in Office 365 and Exchange Online
- FAQ: Public folders
If all of above don’t work, it’s suggested you open a new thread to troubleshoot this issue since the original issue has been resolved. Thanks for your understanding.
Rick