As for why JWST need to circle around the L2 point itself I don't really know, all I know is that this is common for other observatories sent here. And not only circular movements, some have moved in a figure of eight.
Halo orbits are solutions to the three-body-problem similar to the Lagrange points. JWST is principally in orbit around the sun, although this orbit is perturbed by Earth's gravity - three bodies in total. Halo orbits are specific solutions that satisfy two constraints:
1. The orbital period around the sun is identical to Earth's - this is also true for the L2 point itself.
2. The path in a rotating system (i. e. when looking at the L2 point from earth) resembles a periodic orbit around the L2 point.
Note that halo orbits generally aren't elliptic but more of a 3D kidney-shape.
There are other solutions that may look like a figure of eight, or a Lissajous pattern, or orbits that lie entirely in the orbital plane (Lyapunov orbits) but halo orbits are often preferable for operational reasons. Halo orbits are also slightly more stable.
You can even create paths that go from one Lagrange point to another (and back again) without using much if any fuel.
Source: https://www.researchgate.net/publicatio ... int_Orbits
This video illustrates how the halo orbit becomes invisible when viewed from an inertial system: https://youtu.be/IyyQqaF4tNY
Instead, it looks like a slightly wobbly orbit around the sun; this wobbling is the result of Earth's influence. You can't just ignore the Earth and the Sun and pretend as if JWST is orbiting around 'nothing' because the entire thing only works because both celestial bodies are there. (Unlike orbits around a single body, like LEO orbits, where the influence of the sun is negligible). This also makes them relatively susceptible to perturbations from other bodies, like Jupiter, so stationkeeping is required.