I'm not sure it's a collet at all, the bevel is 'wrong' - perhaps it's a tension adjustment of some kind for a shaft? But that doesn't explain the threads.
Photo is misleading then. The bevel looks ok to me. Collet should tighten as it is pulled into the collet holder. That goes ok with the threads on the back of the collet which would act like a drawbar.
It isn't really "essential" that the front taper is significant or not. If the collet holder has enough taper it will tighten the collet regardess. It just won't be a very good fit and it won't provide ideal clamping.
Do you have a micrometer or Caliper? If so, what is the internal thread? What is the ID at the collet fingers? What is the main OD of the collet?
I don't think there is much doubt that it's a collet - the question is only for what.
I make all kinds of home made collets and collet holders to do all sorts of things. It's a pretty common thing a machinist might do. But good luck figuring out what they are for!
Eg, what is this? No fair looking back at my past posts.
Hint - the bolt does not fit the collet but does fit the nut.
It's ok to give up early.
My only point is that your collet appears to be custom made like mine is. If so it may be a huge waste of time to try to figure out what it's for.
Your dimensions might give us a clue but still, the machining marks suggest to me that its most likely a custom collet for some unknown purpose.