The data from the mission will be made public after proprietary periods [1]. They have an archive [2]. I don't expect that the raw telemetry will be made available, but the raw science data in FITS format appears will be available.
[1] https://jwst-docs.stsci.edu/jwst-opportunities-and-policies/... [2] https://archive.stsci.edu/missions-and-data/jwst
Once the data is collected and downloaded it is added to the catalog with all of that metadata attached. Then it's a matter of opening up that catalog to the public, although I'm guessing the downloads will be quite sizeable so the bandwidth could be an issue.
The trick to making this work is to integrate the publishing into the workflow so it doesn't require any additional effort on the part of anyone.