It sounds to me like the caulk is meant to prevent water from getting into the wall, not to prevent water from entering the electrical box. To seal the box, you'll want to use a weatherproof cover with a weatherproof gasket.
If the box is in an area protected from the weather, you can use a cover that is weatherproof when nothing is plugged in.
However, if the box is not protected, you'll want to use a cover that is weatherproof even when things are plugged in.
In my opinion, it's a good idea to use an "in-use" cover for all outdoor receptacles
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
The depth of the jbox is a function of volume which is determined by wire fill. Here's a couple online calculators. They will tell you the cu in required which is labeled for any jbox you can buy. If it's just 1 or 2 14/2 romex cables, any standard lighting jbox should be good.
https://www.constructionmonkey.com/calculations/electrical/boxfill
https://www.ecmweb.com/national-electrical-code/code-basics/article/20886012/box-fill-calculations
How the jboxes are secured depends on your jurisdiction. In my location, all outdoor jboxes (whether new or old work) have to the be secured to studs or attached to cross braces secured to studs. Your location may be different...
The building inspectors here want jboxes flush or just proud with the wall material unless that material is fireproof and wire-safe. Since stucco has metal lathe, that could pose a danger to the wires. Again, that is my local building department's position so your jurisdiction may be different.
EDIT: I did not quote the NEC as I am not electrician. I shared how my local building department (AHJ) interprets the code. I should have been more explicit in recommending you contact your building dept to determine what they require or how they interpret the relevant codes as this will probably be different.