PDM Klein–Gordon oscillators in cosmic string spacetime in magnetic and Aharonov–Bohm flux fields within the Kaluza–Klein theory

In the cosmic string spacetime and within Kaluza-Klein theory (KKT) backgrounds (indulging magnetic Aharonov-Bohm flux fields), we introduce study position-dependent mass (PDM) Klein-Gordon (KG) oscillators. The effective PDM is introduced as a deformation/defect in momentum operator. We show that there are four different ways to obtain KG-oscillator. Two of which readily known other two obtained byproducts settings. Next, provide thorough analysis on corresponding spectra under parametric effects, including curvature parameter's effect. Such used reference/lead model discussion KG-oscillators models: mixed power-law exponential type yields pseudo-confined KG-oscillator KKT (i.e., confined their own manifested Cornell-type confinement), potential. Moreover, extend our discuss non-Hermitian $\mathcal{PT}$-symmetric PDM-Coulombic-type KG-particle KKT14