Go-around - my first sighting

AES wrote
Hard to judge from a passenger seat, but it seemed to take
forever to get the engines spooled back up to full power, and
for the plane to stop descending and start actually climbing.

Yep! If it's not IMC at minimums, we tried to give the PAX as
smooth a ride as possible.

Suppose a commercial airliner is in the late stages of an
approach, and an sudden hard go-around decision is made.
Assuming everything is done right, how much additional altitude
is lost before the airplane levels off and starts climbing?

Under those conditions, very little...perhaps 50' at most.

Bob Moore
ATP B-707 B-727
PanAm (retired)