  Planets orbiting young stars are thought to experience atmospheric
evaporation as a result of the host stars' high magnetic activity. We study the
evaporation history and expected future of the three known transiting
exoplanets in the young multiplanet system K2-198. Based on spectroscopic and
photometric measurements, we estimate an age of the K-dwarf host star between
200 and 500 Myr, and calculate the high-energy environment of these planets
using eROSITA X-ray measurements. We find that the innermost planet K2-198c has
likely lost its primordial envelope within the first few tens of Myr regardless
of the age at which the star drops out of the saturated X-ray regime. For the
two outer planets, a range of initial envelope mass fractions is possible,
depending on the not-yet-measured planetary mass and the stars' spin-down
history. Regarding the future of the system, we find that the outermost planet
K2-198b is stable against photoevaporation for a wide range of planetary
masses, while the middle planet K2-198d is only able to retain an atmosphere
for a mass range between ~7 and 18 Earth-masses. Lower-mass planets are too
susceptible to mass loss, and a very thin present-day envelope for higher-mass
planets is easily lost with the estimated mass-loss rates. Our results support
the idea that all three planets started out above the radius valley in the
(sub-)Neptune regime and were then transformed into their current states by
atmospheric evaporation, but also stress the importance of measuring planetary
masses for (young) multiplanet systems before conducting more detailed
photoevaporation simulations.
