  The exoplanet HD97658b provides a rare opportunity to probe the atmospheric
composition and evolution of moderately irradiated super-Earths. It transits a
bright K star at a moderate orbital distance of 0.08 au. Its low density is
compatible with a massive steam envelope that could photodissociate at high
altitudes and become observable as escaping hydrogen. Our analysis of 3
transits with HST/STIS at Ly-alpha reveals no such signature, suggesting that
the thermosphere is not hydrodynamically expanding and is subjected to a low
escape of neutral hydrogen (<10^8 g/s at 3 sigma). Using HST Ly-alpha and
Chandra & XMM-Newton observations at different epochs, we find that HD97658 is
a weak and soft X-ray source with signs of chromospheric variability in the
Ly-alpha line core. We determine an average reference for the intrinsic
Ly-alpha line and XUV spectrum of the star, and show that HD97658 b is in mild
conditions of irradiation compared to other known evaporating exoplanets with
an XUV irradiation about 3 times lower than the evaporating warm Neptune GJ436
b. This could be why the thermosphere of HD97658b is not expanding: the low XUV
irradiation prevents an efficient photodissociation of any putative steam
envelope. Alternatively, it could be linked to a low hydrogen content or
inefficient conversion of the stellar energy input. The HD97658 system provides
clues for understanding the stability of low-mass planet atmospheres. Our study
of HD97658 b can be seen as a control experiment of our methodology, confirming
that it does not bias detections of atmospheric escape and underlining its
strength and reliability. Our results show that stellar activity can be
efficiently discriminated from absorption signatures by a transiting exospheric
cloud. They also highlight the potential of observing the upper atmosphere of
small transiting planets to probe their physical and chemical properties
