Fusion supports "Named Views", which are shown in the browser. Unfortunately, the API does not currently have support for named view.
Here's a previous post from @kandennti that provides a workaround, but a direct solution in the API will be much simpler and more reliable.
Another possible solution is to do what the named view functionality is doing internally. That is to save all the camera settings for the view orientation you want to save and then apply that camera when you want that view. You could save the camera information in an attribute on the root component, so it's saved with the document.
Again, a named view API would be much simpler.
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Brian EkinsInventor and Fusion 360 API Expert
Website/Blog:
https://EkinsSolutions.com