The spatial extent of a neutrino wave packet is determined by its production mechanism and subsequent decoherence. Prior to decoherence, the emitted particles are quantum mechanically entangled, and only the total energy and momentum are well defined; the decoherence timescale sets a common observable energy uncertainty for all particles. We revisit the recent high-precision measurement of the [7]Li recoil peak following K-electron capture decay of [7]Be to the ground state of [7]Li reported by Smolsky et al. [Nature 638, 640 (2025)]. From the measured width (FWHM = 6.7 eV, sigma = 2.9 eV), a lower bound of 6.2 pm was inferred for the neutrino spatial extent under the assumption of equal momentum uncertainties for the recoiling nucleus and the neutrino. We show that entanglement prior to decoherence does not imply equal experimentally observed momentum spreads. Instead, environmental decoherence (~10^{-16} s) sets a common energy uncertainty that limits the achievable energy resolution, consistent with the observed width of [7]Li peak. This energy resolution translates into markedly different momentum uncertainties for [7]Li and neutrino due to kinematic differences. In particular, the relativistic neutrino acquires a much smaller momentum uncertainty than the nonrelativistic [7]Li. Consequently, the spatial uncertainty of the recoiling nucleus is much smaller than that of the neutrino. We infer a substantially larger neutrino wave-packet spatial extent of order ~30 nm.