One thing you could do is install a whole house surge protector in your breaker box. These typically come with a large $ warranty if something does get blown. They come in may forms, the easiest ones simply install into a single circuit slot in your breaker box. Others hard wire in and have a small box that mounts right next to your breaker box.
Depending on the make / model of your breaker box, there would be various choices.
Strictly speaking, that round metal mounting bracket on the back of the fixture is supposed to be secured to an electrical box.
It can be a shallow box, but it's supposed to be a box. You must protect the wires. You want that new garage to still be there 10 years from now.
I can't really tell from the photo, but the right shallow metal box should fit within that recess on the back of the fixture without you needing to cut a hole in the siding. But if you have to cut a hole, then you have to cut a hole (if you do, rent, borrow or buy a holesaw for your drill big enough for the box).
You could attach the box through to the OSB with screws, although personally, I'd lay a 2x4 flat side against the OSB inside the garage, toenail it into the studs on both sides, and screw the box directly through the OSB into that 2x4. So a stiff breeze or errant basketball doesn't knock your light fixture off the wall. :-)
Drill a hole through the OSB and the 2x4 big enough to feed the cable and to accommodate the clamp that holds the cable in the box. The cable has to be clamped into the box.
Then attach the round mounting bracket that came with the fixture to that box, wire everything up, attach the light fixture to the bracket that you attached to the box. That's the way it's designed.
If it's a metal box, it has to be grounded (screwing the grounded mounting bracket to it will accomplish this).
You also have to secure the cable inside the garage as dictated by your local electrical code.
Finally, I'd use a dose of waterproof silicone or caulk around the box, and then again around the fixture itself after it's mounted, to make sure water doesn't seep inside.
Good luck!
Best Answer
See @Tyson's comment - Let's start with your comment:
Hate to be the bearer of bad news but its not. Note that I and others can see all kinds of things that also need to be repaired electrically. Also in order to pull the meter base and enclosed breaker of the board you want to replace you will need to call your utility company for a disconnect/reconnect. This means that the project will have to be permitted and inspected in most areas of the county (USA).
A good electrical contractor can handle the work including the material to hang it on to fit your location. Beware there may be other damage to structural timber if moisture has penetrated the wall and rotted them out.
What do you consider a reasonable expense? In my area something like this would run around $1500 to $2000 for repair and that would not include repair of any unforeseen damage.
Hope this helps and good luck