Electrical – Is a junction box required in the situation

Move the run over a few feet, which would it stick it beside the air duct (I think there's about 1/2" between the duct and the adjacent stud. Is it safe for them to be so close?)

There is nothing I see in the NEC that puts restrictions on running electrical line near HVAC as long as it meets other code requirements. It must be properly anchored to the structure, meaning that when it is run it should be anchored or stapled to the wall studs. HVAC does not count. In absolutely NO circumstances should you ever run electric line INSIDE of HVAC!

Leave the run as is, move Lord Duckington from his throne, cut away the plaster between the two hole, drill holes in the studs and feed said wire through it, fix mess (I think this wall is load bearing, so this might be a bad idea).

A small hole for electrical line in the middle of the stud will not affect the load bearing capacity of the wall by any meaningful amount. This is safe and probably the best option.

Re-wire so that this run is getting its power from the circuit on the wall behind it. They don't have much on them, so I think combining them is probably safe. In this case, would it be safe to have a few inches of romex going from one box to the next and just connect everything with wire nuts?

This is another option and would probably involve less plaster patching when you are done. The only thing you should make sure of is if the lead line is coming to the switch box. If the power is coming to the receptacle or luminaire rather than the switch then this will not work. Make sure to wire everything properly in parallel if you do this.

Pull off the baseboards, drill a new hole in the floor, and move the box a 6 inches to the left (not sure if the lath is behind the baseboards or not).

If you feel that there is enough room there not taken up by the HVAC system then sure, you could rerun it this way from the basement. In fact, with your tall baseboard you can hide the plaster damage and fishtape it up to the new outlet location. Again, please make sure that there isn't a vent running up that wall stud going to upstairs, which seems likely from your photo.

Move

Lord Duckington I am sure doesn't approve.

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!