>>13355223JWST isn't really going to produce a particularly large amount of data, it will be much less than survey telescopes.
>Or is it in a queue somewhere waiting for someone to look at it?That's not really how astronomical data works. Data can be analysed many times for different purposes. Even if some result is extracted from one set of observations, many more things can be done. Data isn't checked off a list, it exists in an archive. More than half of publications from Hubble data are archival, they use existing observations without obtaining any new data. For some datasets hundreds of papers can be written, they can look at different objects or different properties, and they can combine the data with other observations from other facilities. You can even reanalyse old data with newer analysis techniques. Many results are still being extracted from Hubble data, and that will continue for many years.