Confusion about API purpose and implementation

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Hi,
I am confused as to the how exactly the API lets me interact with Fusion 360. Does the API allow for backend integration, or is it merely something for running scripts on my computer?
To elaborate, I have a platform where users perform calculations and build structures component by component. Users can build models in CAD that are parametrically driven by these equations. This means that when the math changes, the designs can be automatically updated in Fusion 360. For this to be effective, I need to be able to do this on the back end where my server sends this data to the proper model in Fusion 360 and the parameter is automatically updated. There seem to be commands for this in the Fusion 360 API, but I cannot tell where those programs are run. Are they simply run on a persons computer where data is read from excel files or other places or can I send data on the back end?
Also, I found the autodesk forge php platform and that seems to imply that back end communication is obviously available, but the videos and other things in the documentation is a few years old and the PHP SDK and similar things are discussed.