  Gaseous time projection chambers (TPCs) with high readout segmentation are
capable of reconstructing detailed 3D ionization distributions of nuclear
recoils resulting from elastic neutron scattering. Using a system of six
compact TPCs with pixel ASIC readout, filled with a 70:30 mixture of He:CO$_2$
gas, we analyze the first directional measurements of beam-induced neutron
backgrounds in the tunnel regions surrounding the Belle II detector at the
SuperKEKB $e^+e^-$ collider. With the use of 3D recoil tracking, we show that
these TPCs are capable of maintaining nearly $100\%$ nuclear recoil purity to
reconstructed ionization energies ($E_\text{reco}$) as low as 5
$\mathrm{keV_\text{ee}}$. Using a large sample of simulated $^4$He, $^{12}$C,
and $^{16}$O recoil tracks, we find consistency between predicted and measured
recoil energy spectra in five of the six TPCs, providing useful validation of
the neutron production mechanisms modeled in simulation. Restricting this
sample to $^4$He recoil tracks with $E_\text{reco}>40$
$\mathrm{keV_\text{ee}}$, we demonstrate axial angular resolutions within
$8^{\circ}$ and we introduce a procedure that under suitable conditions,
correctly assigns the vector direction to $91\%$ of simulated $^4$He recoils.
Applying this procedure to assign vector directions to measured $^4$He recoil
tracks, we observe consistency between the angular distributions of observed
and simulated recoils, providing first experimental evidence of localized
neutron "hotspots" in the accelerator tunnel. Observed rates of nuclear recoils
in these TPCs suggest that simulation overestimates the neutron flux from these
hotspots.
