I would suggest there is no real difference between the two, as far as stretching goes. An extension spring usually has a hook of some form at each end and the coils are close together in the neutral state (some may require a minimum force before any extension is produced – so have residual internal energy when tightly coiled).

Compression springs don’t have the hooks, so extending them is more difficult, but they would be extended by the same amount if subjected to an extension force as they would if compressed by the same force. Simple physics, but the usual closed coils and machining of flat surfaces would complicate matters.

I suppose a compression spring could be annealed, the outer coils modified to make a hook then rehardened and tempered. It would have a different spring constant if treated the same as the original length would be different. Welding on hooks would add a considerable engineering complication

The same might apply to streching a softened extension coil and doing similar to the above. Dimensions will obviously change slightly for both items.

Might as well start from scratch, I would have thought, in most cases. Car suspension coil springs are often not flatted, and the ends fit a shaped seat.

There is a great deal of difference between theory and practicality, I would suggest.

Did that for the belt tensioner on my smaller bandsaw and it worked a treat.

It also depends on the base metal made from, they all vary. All can be annealed but its the rehardening and tempering thats guaranteed to catch every producer out at any level. You dont know what its made from! end result can be soft to brittle who knows. All spring steels work and perform quite differently from grade to grade, one dont work for another.
You form the hook by heating it, if you can do it in the hardened state its a very very poor spring such as clock wire and the like.

Decent springs are made from annealed steel or stainless then hardened then tempered.
Piano/clock stuff can only be treated as a get me out and worked in the weak hardened and tempered state. Highly unlikely any home user would be able to harden and temper again without it breaking.