We present a study of the photochemistry of abiotic habitable planets with
anoxic CO$_2$-N$_2$ atmospheres. Such worlds are representative of early Earth,
Mars and Venus, and analogous exoplanets. H$_2$O photodissociation controls the
atmospheric photochemistry of these worlds through production of reactive OH,
which dominates the removal of atmospheric trace gases. The near-UV (NUV;
$>200$ nm) absorption cross-sections of H$_2$O play an outsized role in OH
production; these cross-sections were heretofore unmeasured at habitable
temperatures ($<373$ K). We present the first measurements of NUV H$_2$O
absorption at $292$ K, and show it to absorb orders of magnitude more than
previously assumed. To explore the implications of these new cross-sections, we
employ a photochemical model; we first intercompare it with two others and
resolve past literature disagreement. The enhanced OH production due to these
higher cross-sections leads to efficient recombination of CO and O$_2$,
suppressing both by orders of magnitude relative to past predictions and
eliminating the low-outgassing "false positive" scenario for O$_2$ as a
biosignature around solar-type stars. Enhanced [OH] increases rainout of
reductants to the surface, relevant to prebiotic chemistry, and may also
suppress CH$_4$ and H$_2$; the latter depends on whether burial of reductants
is inhibited on the underlying planet, as is argued for abiotic worlds. While
we focus on CO$_2$-rich worlds, our results are relevant to anoxic planets in
general. Overall, our work advances the state-of-the-art of photochemical
models by providing crucial new H$_2$O cross-sections and resolving past
disagreement in the literature, and suggests that detection of spectrally
active trace gases like CO in rocky exoplanet atmospheres may be more
challenging than previously considered.