Hi, welcome to the forum!
Some observations and thoughts:
-First, the feature that the Previous Owner showed you is "Roller Reefing," which was state-of-the-art in the 1950's but is, shall we say, -
"less then ideal" today. Cumbersome, destroys your mainsail, requires a reefing claw, etc. This to say you can ignore it. Set up jiffy-reefing (aka slab reefing) and be done with it.
-In the meantime, you have a broken gooseneck. Here's my suggestion for the weekend - get yourself the biggest bolt that you can find that fits in the aftward hole in that bracket in your first photo. It should be long enough to fit well up into the cast aluminum fitting on the boom. Unscrew the bracket from the mast-side hinge, put the bolt up that aftward hole, secure it with a nut on the aft face of the bracket. Then simply mount your boom onto the bolt. Doesn't matter that the boom is not secured to the bolt, there are no appreciable forces pulling the boom OFF the bolt (to the rear/aft). "Just in case," if you have a vang, then keep it a bit tighter than normal (meaning use it upwind and down!). Otherwise, loop a line thru the "horns" of the aluminum fitting and around the mast, with a bit of slack so the boom can turn. Should hold you for a weekend knockabout.
-For permanent fix - drill teh rivet heads off the aluminum goosenack fitting, put the fitting over the "big bolt" and secure it with washer and either a locknut or TWO regular nuts (so it doesn't come undone one day). Then slip the boom over the gooseneck fitting and rivet it back in place. You'll need a rivet kit. Or you can be like me and tap a hole into the fitting and screw it in (you'll need a tap-and-die kit). Up to you (aluminum is soft).
-OR, you can throw money at the problem (assuming this fits your boom):
https://www.drmarine.com/proddetail.asp?prod=DR116. But IMHO, you'll be happier spending the $$ on a jiffy-reefing setup.
Wishing you fair winds!
Tom