I discovered some asparagus in one of my side gardens that has been growing
way too long to harvest it. I read somewhere that if you let it go, it'll turn
into a feathery fern looking plant, and that's exactly what these are doing. Do
asparagus ferns start out as an asparagus stalk?

No, they are different species, although closely related. Edible asparagus is a
hardy species, not a suitable house plant.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)