The observatory has around 7000 moving parts with complex structures for the primary and secondary mirrors and more importantly, the sunshield that would be used to keep the observatory instruments at a specific low temperature. It will take roughly 30 days for Webb to reach the start of its orbit at L2.
At the end of 30 days, the telescope should have stabilized itself in an orbit around L2. But I would assume it takes that many days for deployment and unfolding everything because of the sheer number of parts and motions involved coupled with things like getting to L2, stabilizing orbit, temperature stability and all the checks for the instruments on board along with the mirror deployment (since it's not one big sheet of mirror).
Here's a link which gives an idea about the logistics involved (along with a cool video series of the journey embedded): https://hackaday.com/2021/11/02/30-days-of-terror-the-logist...
To fathom how complex the sunshield deployment is (and that's just a part of the whole sequence), from the link above:
"Full deployment of the sunshield is without a doubt the sketchiest part of the whole process. The sunshield consists of five separate metalized Kapton sheets, each the size of three tennis courts. Each one must be unrolled, extended to its full size, tightened, and spaced out vertically for the sunshield to do its job. This takes the coordinated action of 140 release mechanisms, 70 hinges, eight deployment motors, about 400 pullies, and nearly 400 meters of cable to accomplish, not to mention the sensors, wiring harnesses, and computers to control everything. It’ll take the better part of two days to complete the sunshield deployment."
The whole thing is just insane.
From this talk by Dr. John Mather: https://www.youtube.com/watch?v=2RLGx_wgyAw
Around 1:47 you can see the number of people involved. 3 space agencies (ESA, NASA, CSA), over 3000 engineers and technicians and 100 scientists worldwide.