I was under the impression that one does not cut a hole this close to the edge of a joist
In the UK, holes must be on the centre-line of the joist. In the US, holes may not be closer than 2" to the edge of a joist.
especially not one this big!
In the UK, hole diameters must not exceed 1/4 the height of the joist (1/3 in the US I think?). The hole in your photo looks like 1/3.
Should I be worried about this joist?
It no longer meets safety standards in the US, UK and probably many other countries.
Because the hole is so close to the top edge it is effectively a notch.
So far as I know, the depth of a notch cannot exceed 1/6th (US) or 1/8th (UK) of the height of the joist. The bottom edge of the hole in your joist looks about a third of the way down the joist.
how would I go about repairing it?
I've seen UK advice to use steel strapping across the damaged section and a foot beyond on each side. They use two-part epoxy to ensure the load is spread across the whole length of the steel reinforcement. The steel needs to be substantial since it has to cope with compressive load.
Others suggest nailing (or screwing or bolting) and gluing reinforcing timber or ply (3/4") to both sides of the damaged section. Extending at least 12" beyond the damaged area. Nails are generally better under shear loading than are screws.
I don't know what is acceptable in the US.