You can find a socket which fits the bolt. I think we used SAE not metric socket. Maybe 9/16" or 7/8" size.
On most of these vintage 1970's pianos, often the rear legs were secured with lag screws, and the
front legs used machine bolts. Also, the rear leg itself may be taller than the front legs. You'll know when you
set the piano up and it's tilted. Don't ask me how I know... <g>.
Beware, as a piano mover found out the hard way....do not use lag screw on front legs!
It will go up into the cheek blocks and split them!!
As to the leg separation, this is a failed glue joint. When you take the leg off, you'll see it's joined like the pillars on
a pedal lyre. Likely a round dowel with a wedge driven into it to secure the lower tapered let with the 'head', or upper
part of the leg. This will have to be taken apart and reglued.
Both the bolts not being tight and the glue joint failure have attributed to the 'wobbly' piano.