Sifting exoplanet signals from noise and reviewing recent habitable planets

[AveryNW]

I'm an amateur astronomer fascinated by the progress in exoplanet discovery, especially with missions like TESS and the upcoming James Webb observations. I understand the transit and radial velocity methods, but I'm trying to wrap my head around how researchers actually sift through the massive datasets to distinguish a true planetary signal from stellar noise or instrumental artifacts. For those who follow the field closely, what are some of the most promising recent discoveries of potentially habitable zone planets, and what makes their detection and confirmation particularly robust or interesting?