Can anyone provide me with the proper request to soap endpoint to somehow enable mail access on public folders?
Does your question is "how to send a request to mail-enable access to public folder via EWS"?
If yes:
Public folders provide a shared repository of items that users in your organization can access. Office 365, Exchange Online, and on-premises versions of Exchange starting with Exchange 2013 introduce a new architecture for public folders.
Most of the core EWS operations support public folder access. You can use the folder and item operations and the EWS Managed API methods listed in the following links to work with public folders:
Public folder access with EWS in Exchange
Route public folder content requests
Route public folder hierarchy requests
note: You only could use the EAC or Exchange Management Shell to mail-enable or mail-disable a public folder