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The two planetary systems, TOI-942 and TOI-421, share many similar characteristics, apart from their ages (50 Myr and 9 Gyr). Each of the stars hosts two sub-Neptune-like planets at similar orbits and in similar mass ranges. In this paper, we aim to investigate whether the similarity of the host stars and configuration of the planetary systems can be taken as proof that the two systems were formed and evolved in a similar way. In paper I of this series, we performed a comparative study of these two systems using three-dimensional (3D) modelling of atmospheric escape and its interaction with the stellar wind, for the four planets. We demonstrated that though the strong wind of the young star has a crucial effect on observable signatures, its effect on the atmospheric mass loss is minor in the evolutionary context. Here, we use atmosphere evolution models to track the evolution of planets in the younger system TOI-942 and also to constrain the past of the TOI-421 system. We demonstrate that despite all the similarities, the two planetary systems are on two very different evolutionary pathways. The inner planet in the younger system, TOI-942, will likely lose all of its atmosphere and become a super-Earth-like planet, while the outer planet will become a typical sub-Neptune. Concerning the older system, TOI-421, our evolution modelling suggests that they must have started their evolution with very substantial envelopes, which can be a hint of formation beyond the snow line. [ABSTRACT FROM AUTHOR]

At young ages, when radiation from the host star is high, and the planet is hot and inflated after formation, planetary atmospheric mass-loss can be extremely strong compared to older planets. In turn, stellar winds are faster and denser for young stars compared to evolved main-sequence stars. Their interaction with escaping planetary atmospheres can substantially affect atmospheric mass-loss rates, as well as the observable signatures of escaping atmospheres, with both effects expected to occur differently for young and evolved planets. We perform a comparative study of two systems around stars of similar masses but very different ages (50 Myr and 9 Gyr): TOI-942 and TOI-421. Both stars host two sub-Neptune-like planets at similar orbits and in similar mass ranges, which allows a direct comparison of the atmospheric escape and interactions with the stellar winds in the young and old systems. We perform the 3D atmospheric modelling of the four planets in TOI-942 and TOI-421 systems and make the theoretical predictions of possible observational signatures in Ly α absorption. We find that accounting for the stellar wind interacting with planetary atmospheres is crucial for the interpretation of the observations for young planets. Additionally, we show that a particular energy distribution along the XUV spectra has a minor effect on the atmospheric mass-loss rates, but it is of crucial importance for modelling the Ly α absorption and therefore for interpretation of observations. [ABSTRACT FROM AUTHOR]