Hi.
Looks like the worm portion is made separately from the tip portion and either punched or soldered in place at the same time the butterfly is soldered to the tip.
Very strange way to do it indeed.
I'd soft solder the parts back together. Carefully obviously, so the nickel (?) plating doesn't start to flake.
Edit: After a good nights sleep, a thought occurred to me

. I've seen a tuner like that, a long time ago. The hole could be a "rivet" hole and the rest of the rivet is in the worm shaft. The best way to repair this (if You don't want to solder is to drill a new hole onto the shaft and install a new rivet.
Repairing the tuners may be for vain though. The A tuner shaft end is almost out of it's socket, and the rest of them are more or less worn as well. Anything's repairable, but it'll cost dearly.
Way better option than an exessive repair is to buy new tuners and keep the old ones in a shelf for future restoration.
Regards
Sam