I don’t think that you screwed up.
You discovered that your reservoir was a bit low. Ok - empty. That is a good catch. It is possible that the reservoir or the siphon hose to the radiator is leaking - that is still bad for the cooling system as when the fluid expands when hot, it cannot suck it back - so you end up with air space which fills with steam. It seems like you have caught it just before that happened.
When was the last time that you checked the fluid level ? Weeks, months, years ? My latest bike, the level hardly dropped at all from one year to the next. But the fluid would be flushed and changed every couple of years.
There is a drain hole on the right hand side of the bike which normally gives a tell tale sign when fluid is leaking past the mechanical seal - I think for the water pump. There’s no point looking for it ‘cos from 2008 Honda had got so fed up with paying up for claims due to evidence of leakage at that hole that were unnecessary - the mechanical seal does seep a little fluid as a matter of course - that they put a drain pipe and hose in its place. Yours will have that drain hose.
Fill up the reservoir again, fill the radiator, bleed the system (read the manual ‘cos I’ve forgotten how - but it involves leaving the cap off and revving the engine. Air burps up to the filler cap and the radiator level goes down. Top it up again. Something like that )
Clean up old stains - signs of fluid. Run the engine. Look for signs of leaks around the radiator hoses - the inlet/outlet pipes are VERY thin , VERY soft alloy, and over tightening of the hose clamps will turn the pipe into an oval. Also around the radiator fins, filler cap and reservoirYou might want to check if that had happened. They can be straightened out into a proper circle (!). I made that overtightening error once, and sorted it with a Stanley elliptical handled screw driver handle, gently rotating while gently pressing into the pipe end. By the way NEVER try to remove any hose by pulling - that increases the grip on the pipe. Hoses have to be pushed off.
Anyway - take it for a short ride or simply let it run through a few cycles of the radiator fan turning on and off. Rev the engine. But a short ride would be ok, providing you keep an eye on the reservoir level. And take the precaution of having top up fluid with you. You can ride the ST1300 without fairing in place, but you need to stop the nose fairing from flapping around where the pockets would be. Leave it standing where you will see evidence of leaks until it cools. Check the reservoir level. Has it dropped ? How much ? Top it up. Repeat for a longer short ride.
If there is no evidence of anything - I’d be surprised, but the possibility of a screw up remains. But if so, you caught it. Everyone screws up. Most don’t admit. Most make stuff up rather than admit that they don’t know. If you read some of my past post, I don’t care about admitting to blunders. My assumption after finishing a service always that I have missed something - So I’ll take a break, leave it overnight (dreaming helps here, the answer often pops up in a dream about (say) the back wheel dropping out - which may mean I forgot to torque the axle bolt. - I have a small stool in the garage and sit and look at the bike and work through everything that I should have done. It used to reveal something. It rarely does now, but I still do it ‘cos I am not perfect AND I am getting older.
I used to be a teacher. Kids (we are not supposed to call them ‘kids’, but I’m retired now) have grown up frightened to admit mistakes or to say they don’t know, or that they don’t understand. One of my priorities was to encourage them out of this. I’d make deliberate mistakes. Their job was to spot them. It became a game. Sometimes I made genuine mistakes and I’d own up if they spotted one of those - a deliberate mistake that I didn’t know about.
Like the kid who asked “what is ‘deliberate’ sir ?” Oops !
