Could 48V arc across this small gap?

Even a very small gap is sufficient to stop quite a bit of voltage. IPC-2221B would specify 0.6mm for 48V for an exposed gap on a PCB.

Breakdown voltage of an air gap is much higher than that-- 48V will hardly start an arc over any non-microscopic gap.

Of course if you get conductive dirt or liquid on it, all bets are off. For example, by using plumber's solder with acid flux.

No problem, Air gap is >1kV/mm with humidity and a bit less with dust which would just burn if you had an inductive transient exceed this level. But then you need reverse LED protection if you had inductive switching.

The wire looks well tinned and bonded. You can always add a 1cm stretch of Polyurethane rigid plastic (subfloor adhesive) for wire strain relief as well for the solder pad protection. This also acts as short circuit protection.

The copper bottom surface should be greased & screw clamped to a heatsink.