  Future astrophysics missions will seek extraterrestrial life via transmission
and direct imaging observations. To assess habitability and biosignatures, we
need robust retrieval tools to analyze observed spectra, and infer surface and
atmospheric properties with their uncertainties. We use a novel retrieval tool
to assess accuracy in characterizing near-surface habitability and
biosignatures via simulated transmission and direct imaging spectra, based on
the Origins Space Telescope (Origins) and LUVOIR mission concepts. We assess
our ability to discriminate between an Earth-like and a false-positive O$_3$
TRAPPIST-1 e with transmission spectroscopy. In reflected light, we assess the
robustness of retrieval results to un-modeled cloud extinction. We find that
assessing habitability using transmission spectra may be challenging due to
relative insensitivity to surface temperature and near-surface H$_2$O
abundances. Nonetheless, our order of magnitude H$_2$O constraints can
discriminate extremely desiccated worlds. Direct imaging is insensitive to
surface temperature and subject to the radius/albedo degeneracy, but this
method proves highly sensitive to surface water abundance, achieving retrieval
precision within 0.1% even with partial clouds. Concerning biosignatures,
Origins-like transmission observations ($t=40$ hours) may detect the
CO$_2$/CH$_4$ pair on M-dwarf planets and differentiate between biological and
false positive O$_3$ using H$_2$O and abundant CO. In contrast, direct imaging
observations with LUVOIR-A ($t=10$ hours) are better suited to constraining
O$_2$ and O$_3$, and may be sensitive to wavelength-dependent water cloud
features, but will struggle to detect modern Earth-like abundances of methane.
For direct imaging, we weakly detect a stratospheric ozone bulge by fitting the
near-UV wings of the Hartley band.
