Welcome and conratulations on your ST1300.
I agree with
@wjbertrand - ABS light on is normal - until you move off a short distance.
ABS button - that is something that exists on some models of the ST1100. The ST1300 doesn't have one. ABS is active all of the time.
When you do a search on the forum, (eg for ABS) it will find posts relating to both bikes. One clue to which thread you are looking at is the breadcrumb trail - put there to help you find your way back to it later. Like this - highlighted in a red rectangle.
Another way is to check the original poster's avatar on the left hand side. Most of us have added the type of bike that we own. eg my details under my photo are shown below - and you can see the rest in the left margin of this post.
Your post was very clear - you stated model and year in the original post - so no such problems !
Clutch, Neutral and Centre stand switches all interact to stop you driving off with the side stand down.
Briefly, the engine will always run if the bike is in neutral (green light shows on dash).
If in gear, the engine will cut out if the sidestand is put down - with or without the clutch lever pulled in.
With the sidestand up and the bike in gear, the engine will not fire up unless the clutch lever is pulled in.
See if you can move the bike when it is in gear and with the clutch lever pulled in, that is normal. If it is hard work, or not possible, then the clutch is not disconnecting the engine from the rear wheel. You may want to confirm this behaviour with the bike on the centre stand, bike in gear and try rotating the back wheel with the clutch lever pulled in. - Use your foot, or get some help to rotate the back wheel.
Note that it is perfectly normal for the rear wheel to start to turn if the bike is on the centre stand, in neutral with the engine running. It starts slowly and gradully picks up speed. It is just the drag on the various moving parts moving close to each other in their oil bath. Press the brake pedal and it stops easily.
There is a fair chance that your clutch needs bleeding. The bleed valve is behind the fairing - just in front of the left hand side swinging arm bolt, Peeping out from behind the silvered frame spar. You might be able to get to it just by remving the lower panel on the left hand side, and the two lower faring bolts behind the tip over bar cover - and gently easing out the lower fairing. But it may be a bit fiddly. Don't take that as gospel anyway - someone will put me right if necessary - If I ever need to bleed the clutch, I will have a load of other stuff to do, and I prefer to take the faring off completely.
The clutch is easy to bleed with a non-return bleed valve and length of tubing and a container of fresh DOT 4 brake fluid.
Please keep us informed what you find out and how you get on.