Its could be the seals but hard to tell from photographs but not sure if there is a problem with the seals and what your seeing here is the modern day practices of car manufacturing.
Happens on my KIA sometimes and previously on my VW Golf and it happens because cars don’t have rain gutters any more so water collects along the top edge of the door and when you open the door it falls into the inside of the car even though the inner rubber seal should catch it it does splash sometimes.
Whatever get them to check the seals anyway as warped doors are not uncommon or seals not seated properly.
Like you I find it very hard to the wipe the inside of the screen using just my right hand and with the long rake many screens have these days but auto demist sorts most problems with A/C on as GG suggested,