
Short answer is no, this cannot be done out of the box.
The standard general ledger Setup API in BC is read-only by design. The error "Entity does not support modifying data" is exactly that, Microsoft has not exposed PATCH on the General Ledger Setup. It is a singleton setup table and the standard API page does not allow write, even if Page 118 is exposed as a web service with Allow Write turned on, OData still treats it as a collection and blocks PATCH.
So the two options are:
Either expose Page 118 through a custom API page in AL, with the right entity name and a key, and PATCH against that. To enable the PATCH method, the custom API page must use SystemId as the ODataKeyFields. This gives the OData endpoint the unique identifier it needs to update the record.
Or use an Automation Flow / a simple codeunit exposed as a bound action, but that also needs AL.
There is no Postman-only, configuration-only way to update General Ledger Setup. The "Allow Write" trick on the SOAP/OData page service does not bypass the singleton restriction on this particular page.