  The TRAPPIST-1 system is a priority target for terrestrial exoplanet
characterization. TRAPPIST-1e, residing in the habitable zone, will be observed
during the JWST GTO Program. Here, we assess the prospects of differentiating
between prebiotic and modern Earth scenarios for TRAPPIST-1e via transmission
spectroscopy. Using updated TRAPPIST-1 stellar models from the Mega-MUSCLES
survey, we compute self-consistent model atmospheres for a 1 bar prebiotic
Earth scenario and two modern Earth scenarios (1 and 0.5 bar eroded
atmosphere). Our modern and prebiotic high-resolution transmission spectra (0.4
- 20 $\mu$m at $R \sim$ 100,000) are made available online. We conduct a
Bayesian atmospheric retrieval analysis to ascertain the molecular
detectability, abundance measurements, and temperature constraints achievable
for both scenarios with JWST. We demonstrate that JWST can differentiate
between our prebiotic and modern Earth scenarios within 20 NIRSpec Prism
transits via CH$_4$ abundance measurements. However, JWST will struggle to
detect O$_3$ for our modern Earth scenario to $> 2\,\sigma$ confidence within
the nominal mission lifetime ($\sim$ 80 transits over 5 years). The agnostic
combination of N$_2$O and/or O$_3$ offers better prospects, with a predicted
detection significance of $2.7\,\sigma$ with 100 Prism transits. We show that
combining MIRI LRS transits with Prism data provides little improvement to
atmospheric constraints compared to observing additional Prism transits. Though
biosignatures will be challenging to detect for TRAPPIST-1e with JWST, the
abundances for several important molecules - CO$_2$, CH$_4$, and H$_2$O - can
be measured to a precision of $\lesssim$ 0.7 dex (a factor of 5) within a 20
Prism transit JWST program.
