This paper investigates continuous representations of steering vectors over frequency and microphone/source positions for augmented listening (e.g., spatial filtering and binaural rendering), enabling user-parameterized control of the reproduced sound field. Steering vectors have typically been used for representing the spatial response of a microphone array as a function of the look-up direction. The basic algebraic representation of these quantities assuming an idealized environment cannot deal with the scattering effect of the sound field. One may thus collect a discrete set of real steering vectors measured in dedicated facilities and super-resolve (i.e., upsample) them. Recently, physics-aware deep learning methods have been effectively used for this purpose. Such deterministic super-resolution, however, suffers from the overfitting problem due to the non-uniform uncertainty over the measurement space. To solve this problem, we integrate an expressive representation based on the neural field (NF) into the principled probabilistic framework based on the Gaussian process (GP). Specifically, we propose a physics-aware composite kernel that models the directional incoming waves and the subsequent scattering effect. Our comprehensive comparative experiment showed the effectiveness of the proposed method under data insufficiency conditions. In downstream tasks such as speech enhancement and binaural rendering using the simulated data of the SPEAR challenge, the oracle performances were attained with less than ten times fewer measurements.