"I do not know the cost of this device, but the electrician that
installed it mentioned that a 15 ampere GFCI circuit breaker would be
about 130$us. "

A GFCI breaker should cost about 1/3 of that, unless that price
includes installation. Also, it's not clear to me why an electrician
would put a seperate GFCI in it's own box in the basement to service a
bathroom fan instead of just putting in a GFCI breaker. The later
would seem easier, less confusing, and less labor.