We present the first statistical analysis of kinematically-resolved, spatially-extended Ly$alpha$ emission around $z = 2-3$ galaxies in the Keck Baryonic Structure Survey (KBSS) using the Keck Cosmic Web Imager (KCWI). Our sample of 59 star-forming galaxies ($z_mathrm{med} = 2.29$) comprises the subset with typical KCWI integration times of ~5 hours and with existing imaging data from the Hubble Space Telescope and/or adaptive optics-assisted integral field spectroscopy. The high resolution images were used to evaluate the azimuthal dependence of the diffuse Ly$alpha$ emission with respect to the stellar continuum within projected galactocentric distances of $lesssim 30$ proper kpc. We introduce cylindrically-projected 2D spectra (CP2D) that map the averaged Ly$alpha$ spectral profile over a specified range of azimuthal angle, as a function of impact parameter around galaxies. The averaged CP2D spectrum of all galaxies shows clear signatures of Ly$alpha$ resonant scattering by outflowing gas. We stacked the CP2D spectra of individual galaxies over ranges of azimuthal angle with respect to their major axes. The extended Ly$alpha$ emission along the galaxy principal axes are statistically indistinguishable, with residual asymmetry of $le$ 2% ($sim 2 sigma$) of the integrated Ly$alpha$ emission. The symmetry implies that the Ly$alpha$ scattering medium is dominated by outflows in all directions within 30 kpc. Meanwhile, we find that the blueshifted component of Ly$alpha$ emission is marginally stronger along galaxy minor axes for galaxies with relatively weak Ly$alpha$ emission. We speculate that this weak directional dependence of Ly$alpha$ emission becomes discernible only when the Ly$alpha$ escape fraction is low. These discoveries highlight the need for similar analyses in simulations with Ly$alpha$ radiative transfer modeling.
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