As explained in Street Magic,
An astral shadow is a "drab reflections of lifeless objects present in the
physical world." (p. 112 - Shadows)
p. 114 - Astral Visibility :
Shadows of physical objects in the astral plane may be drab and
insubstantial, but they are still opaque and can prevent targeting. Items that are transparent or mirrored in the real world
(like a car window) simply impair visibility as astral shadows.
So in this scenario, the adept could not see through the window since glass, as any other astral shadow, is opaque to Astral Perception.
The only exception to shadows impairing astral visibility is clothing (Street Magic p.112 - Auras) :
clothes and other non-living objects are often outshone by the brightness of the wearer’s aura
Contrary to cyberware which, by its intrusive nature, leaves shadowy gaps
in auras, which are easily perceived by an Assenssing check with 2+ successes, while bioware, being living tissue, needs at least 4 successes (SR4A p.191 - Assensing Table)
EDIT : the sentence "simply impair visibility" being vague at best, let me extrapolate from other sources :
SR4A p.191 - Astral Perception :
Astral perception is a psychic sense that is not linked to the character’s physical sight.
While there may be some material "simply impairing" (that is : a material which you can astrally "see" through, but with some malus) a psychic sense, I can think of no reason why simple glass would be such a material. Glass' ability to let light go through itself doesn't justify an ability to let emotions do the same.