If HP³ detects water, it will be done indirectly through thermal conductivity or specific heat. It has no sensor that directly detects water, such as a chromatograph or mass spectrometer (nor room for such).
The paper you cite above was published in 2011. It was written before HP³ was chosen in 2012 for InSight:
The mole design goes back to the PLUTO mole (PLanetary Underground Tool) developed for the unsuccessful Beagle-2 mission. An evolved design was manifested to fly as part of the Humboldt experiment package on the ExoMars mission which was canceled in 2009 as part of the reformulation of the ExoMars mission concept. HP³ was selected by NASA as a payload for the InSight lander in 2012 since the development work completed under ExoMars already advanced to a detailed instrument concept ready to press into manufacture and testing.
The last sentence of the above quote makes it clear that NASA wanted a technology that was ready to go. Adding more sensors to HP³ would have added a lot of development and testing time.
The "mole" has heating foils, temperature sensors, and tilt sensors. Its ribbon cable has additional temperature sensors. Other than the older paper you cited, I find no evidence of sensors for electrical permittivity and conductivity.
The interior of the mole can be broken down in three sections: the hammering mechanism, the Active Thermal Measurement Suite (heater foils and sensors), and the Static Tilt Sensors (STATIL) residing in the upper part of the mole’s body. Damping springs are installed between the hammering mechanism and the sensing equipment to lessen the loads transferred to the instrumentation.
Even if something isn't directly measured, it's fairly common for scientists to publish journal articles that draw conclusions from other data. For example, there have been many conclusions about the density, temperature, and composition of exoplanets, even if those factors have never been directly measured. No doubt that years from now someone will look at old HP³ data and draw conclusions about the existence of water.