There’s not realistically an option to repair a standard Gates-style belt drive in the field short of having a spare belt. Any kind of ‘splice’ wouldn’t be able to actually reliably join the two ends of a severed belt (it would fail again very quickly due to the tension requirements for it to actually work well), and even if it could it would usually shorten things far too much to be usable (short of active sabotage, it’s really rare for a belt to just cleanly ‘snap’ at one spot, it usually loses teeth and the layers partially delaminate as well, so you end up with a long stretch of unusable length, often 5% or more of the overall length of the belt).
And spare belts are, in reality, not actually that easy to carry. They are definitely light, but they’re relatively big and you can’t bend a Gates belt beyond a certain radius without risking damaging it because of the stiffness, which makes it unwieldy to actually carry one on a bike. Imagine trying to carry a wire-bead tire with an extremely low TPI and you’ll get the general idea.
The ‘conventional’ approach is to stay on top of maintenance and get the belt replaced when you start to see the bright blue inner layer peeking through the teeth (it’s there specifically to be a highly visible wear indicator) and ensure you have proper tension on the belt every time you install the rear wheel. Almost all catastrophic failures of these belts happen because they’re either far too worn down, or the belt is way too lose (which can cause skipping, which in turn wears out the teeth super fast and can cause whole runs of teeth to just shear off).
I go a step further than this myself with my commuter that has a Gates drive, and have a (waxed) chain, sprocket, and chainring ready and waiting in case the belt fails so that I have a usable bike until I can get a new belt shipped, and I have sufficient tools to replace all of it myself, though I don’t generally carry any of it with me when riding (I rarely ride far enough from home for this to be a worry, and I very actively stay on top of maintenance so it’s unlikely I’ll ever actually be running a belt that’s sufficiently worn to be a risk, except possibly to get the bike to my LBS for a replacement). If I were going long-distance though, I would definitely include those parts in my kit, plus a chain whip and strap wrench to swap the sprocket, and appropriate Allen wrench for the chainring so that I could swap everything in the field.