As of 1/17/22 the solar shield has successfully deployed, as well as all the telescopic mirror panels. However, it is far from operational. It has traveled about 824,000 miles from earth (by comparison, the moon is about 235,000 miles away) and now has only about 76.000 miles to each its proper orbit spot. All the mirror panels will then be slowly adjusted over a period of several months until they are all perfectly aligned so that all the panels will operate as a single large mirror. Then it will start taking infrared pictures. Some of the very first pictures may be of the earth to measure world wide temperatures of the entire surface of the earth to add to climate change data. They also want to study a super massive black hole that was recently discovered in a near by "mini" galaxy.
In other words it will first be tested on "near by" objects before it starts looking back in time to the early universe where we will see it more detail than ever before because it will see though much of the dust surrounding and with the galaxies. We may learn more about how the earliest galaxies were formed. However, what interests me the most, as I mentioned in another post, it the possibility that the JWST might discover signs of life on distant planets.