Yikes, there's too much to unpack here but I think what you're referencing is the images that are created from the archive. Are you familiar with the 3 stages of the pipeline?

Remember too, there are 10 detectors in the JWST, and the limit in the SSR is only 65GB, so much of the processing is done on board to reduce data excess. Tons more info can be found here: https://jwst-docs.stsci.edu/jwst-general-support/jwst-data-volume-and-data-excess

More info on the data pipeline can be found here: https://jwst-docs.stsci.edu/jwst-science-calibration-pipeline-overview/stages-of-jwst-data-processing#:~:text=The%20processing%20of%20JWST%20data%20goes%20through%203,%28slope%29%20images.%20Stage%202%20calibrates%20the%20slope%20images.

Also keep in mind JWST does thousands of exposures using many of the instruments. That data is accumulated in the SSR and is streamed every 12 hours or so to earth.

That's just not true. Because time is limited, they use JWST to point at a sector, and then use it to capture hundreds of composite images. Those images are processed by humans using algorithms, and in a lot of cases machine learning.

I think you're coming from the standpoint of a telescope on Earth, which has an extremely narrow view of space. With JWST, the images it takes are truly, truly massive and produce hundreds of gigabytes of data, which can be used to produce images.

It's both. JWST produces imaging data without any intervention by a human. Generally, that data is modeled by a human, but there's also a huge amount of these findings that are discovered by an algorithm, and have little to no human interaction to find.