Sounds too good to be true. How did you manage to dock with L2?
Where is it stated by NASA or ESA that JWST "docks" at L2. I have only heard you say that.
ESA/NASA have repeatedly told the world that JWST has arrived at L2 and started to orbit around L2, even if L2 has no mass to be orbited around. I just understood it that JWST had stopped and docked at L2. Asking NASA/ESA for clarification is hopeless. No answers. Try yourself!
I am sure I would get nothing from them if I were also to ask them an absurd question.
There is no stopping, and no docking.
The blue line is Earth, and the yellow the JWST.
The JWST orbits the Sun at a faster speed than the Earth, such that its orbit (which is larger than the Earth) matches the Earth's, and remains at the same point (L2) relative to the Earth.
Under a geocentric model it would appear to have stopped at L2. The geocentric model is wrong. That you only accept a geocentric model is your problem, not NASA's, and hence them filing your question under spam.