I'm no expert on this subject but I can give you some ideas on where to look. Is that check engine light flickering or is it solid (cameras tend to make LEDs flicker on video)?
I would check your battery voltage first with a multimeter. I know you don't have one at the moment but I would just spend the money for one, they're so worth it. You'll use it for the rest of your life.
Make sure you torque down the bolts on your battery terminal. Having them loose can cause all sorts of weird problems and make diagnostics difficult.
If the engine light is flickering, that could show that a harness connector got loose somewhere . I would remove body panels (not sure if it's possible on a Z125) and check every single harness connector on the bike to make sure it didn't pop out or anything from impact. Notably the starter motor harness, and your ignition coil (you can check by disconnecting your spark plug if it works too). If you got spark but it's not turning over, could be the starter. I would also look on the main harness from your ECU to see if it got loose.
If you take that bolt cover on your crankshaft case and turn your crankshaft and you're able to turn it over and feel compression, then there's a good chance your engine is good and something is messed up with the starter assembly. Take that with a grain of salt because I've never had an issue like this but that's where I'd look at since it's fairly non-intrusive.
Hope it helps! Report back to us, I'm curious to hear how it goes & hope it gets fixed