V1298 Tau with TESS: Updated Ephemerides, Radii, and Period Constraints from a Second Transit of V1298 Tau e

V1298 Tau is a young (20-30 Myr) solar-mass K star hosting four transiting exoplanets with sizes between 0.5 - 0.9 $R_J$. Given the system's youth, it provides a unique opportunity to understand the evolution of planetary radii at different separations in the same stellar environment. V1298 Tau was originally observed 6 years ago during K2 Campaign 4. Now, V1298 Tau has been re-observed during the extended mission of NASA's Transiting Exoplanet Survey Satellite (TESS). Here, we present new photometric observations of V1298 Tau from the 10-minute TESS Full-Frame Images. We use the TESS data to update the ephemerides for V1298 Tau bcde as well as compare newly observed radii to those measured from the K2 light curve, finding shallower transits for V1298 Tau bcd in the redder TESS bandpass at the $1-2\sigma$ level. We suspect the difference in radii is due to starspot-crossing events or contamination from nearby faint stars on the same pixels as V1298 Tau. Additionally, we catch a second transit of V1298 Tau e and present a new method for deriving the marginalized posterior probability of a planet's period from two transits observed years apart. We find the highest probability period for V1298 Tau e to be in a near 2:1 mean motion resonance with V1298 Tau b which, if confirmed, could make V1298 Tau bcde a 4 planet resonant chain. V1298 Tau is the target of several ongoing and future observations. These updated ephemerides will be crucial for scheduling future transit observations and interpreting future Doppler tomographic or transmission spectroscopy signals.