there are T nuts on the back...it's not uncommon for them to spin....I'm dealing with one myself
If you can....drill the bolt head out...getting a grip on it is always the problem.
the reason it's spinning..the wood has deteriorated far enough on the inside of the door to release the teeth on the nut
knowing that a new handle is $12.00 and the t-nuts are available at your local hardware store....
the problem becomes not damaging the siding...if you can drive a small, flat screwdriver between the head of the nut and the seat in the handle it is a bit easier
or in your case, drilling out the tumbler...
knowing that the t-nut is spinning....expect some rot in the door (not uncommon)......I'm considering a 1/4" flat aluminum plate, threaded for the handle bolts.....