The only "safe" - as in entirely beyond criticism - way to fix that is to have the dropout replaced. As it seems to be a steel frame, its doable enough. A partial repaint and the bike is as good as new.
No drama at all to a frame builder, a modest challenge to a generic metal worker.
Someone not working bikes regularly would need to create some sort of jig to get the alignment right.
Apart from that metal is metal.
It'll cost some though, particularly if you want a blend-in paintjob.

Me, I'd remove the axle adjustment screw, grind a V-shaped groove along the crack on both sides. Stick an axle sized bolt at the open end of the dropout, use some washers and a nut to maintain alignment. Then use whatever arc welder that was handy to run a bead through the ground out groove to fill it up. A quick swipe with an angle grinder to get the dropout face flat and call it done. Maybe a dab of primer.
With luck, the adjustment screw would still fit. If it didn't, I'd try to retap it. If that didn't work I'd just consider it a "war wound" and do without it.