This article may interest you: It's what the Earth would look like through JWST at 40 light years away.

However, none of the planets in our solar system are particularly amenable to being detected by an instrument like JWST, see here and here. JWST is best at finding exoplanets via transit light curves, and these mostly find "Hot Jupiters" or "Warm Neptunes", planets with larger masses that are much closer to their star than any of the giants in our solar system are to the sun. JWST can also do direct imaging of planets, but that works best for planets that are very far out like Neptune, but also massive, ~10x the mass of Jupiter. So our solar system is not a very good candidate for finding anything at all with just JWST. They'd be most likely to find Jupiter through radial velocity measurements using a optical telescope with better spectral resolution, for example the Keck observatory has likely detected a Jupiter twin.