Phase Transition and Nuclear Symmetry Energy from Neutron Star Observations -- In Light of PSR J0614--3329

The possible occurrence of a first-order hadron-quark phase transition (FOPT) in neutron-star interiors remains an open question. Whether such a transition can be directly tested with improved observations is a key challenge. Here, we incorporate the latest constraints, especially a new NICER radius measurement for PSR J0614--3329, into a nonparametric Gaussian Process (GP) EOS framework that explicitly includes a first-order transition. We find a Bayes factor of B≈2.3 when comparing models with and without an explicit phase transition, marginally favoring its presence. At $68%$ credibility, the transition onset density nPT is either below 2\,nₛ (corresponding to masses 1\,M_, with density jump Δn~0.5\,nₛ) or, more prominently, above 4\,nₛ (near the central density of the heaviest NS, with Δn~3\,nₛ), where nₛ represents the nuclear saturation density. In addition, by using symmetry-energy expansion at low densities (<1.1\,nₛ), we infer a slope parameter L=40.2+19.3-14.3 MeV, in good agreement with nuclear-experiment values. Intriguingly, L correlates positively with the radius difference between 1.4\,M_ and 2.0\,M_ stars.