Attempts via REST:
Currently running on Confluence 7.3.2, it seems space permissions can't be expanded via
/rest/api/space/<SPACE_KEY>?expand=permissions
compared to Confluence Cloud where it yields permissions.
Attempts via SOAP:
The SOAP endpoints yields different XML on 7.3.2 compared to another 5.7 version I tested. I didn't manage to generate bindings (in C#) using the 7.3.2 WSDL.
On 5.7:
On 7.3.2
Welcome to the Atlassian Community @Julien St-Pierre Fortin
In Confluence Server REST API documentation, I couldn't find "permissions" property for /rest/api/space endpoint, so seems it is not made available by Atlassian. You can also confirm that by raising a support ticket to them directly.
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