If you have had your rear caliper off, then you might want to check out this document - download the pdf in post#1.
This deals with most of the easily fixable problems created by having the brakes / wheel off. Usually the little things that are not commonly known about.
A close hands-on look at the Honda ST1300 braking system. These are personal observations about the things that can go wrong, why they go wrong and what can be done to keep things working sweetly. Updated April 2020 and to address more recent observations, to include information about the SMC...
www.st-owners.com
Then there are issues at the front wheel. eg Not many people new to the ST1300 know that you MUST follow a particular sequence when installing the front wheel. If you don't then that can cause the SMC to operate, which causes the rear wheel to drag.
Animated sequence to show the correct procedure when installing the front wheel into the forks of a Honda ST1300. The right hand side of the bike is the side with the brake lever. Left is the clutch lever side. This is the convention used in the Honda manuals. The video and the photo below...
www.st-owners.com
And of course - check that the SMC is working properly - when you apply it by hand - as if you were applying a brake lever - the back wheel should stop turning and when you release the SMC it should free up instantly. Given the age of the bike, it has to be suspect - but there are so many 'fingers' issues where things have not been assembled correctly. Having too much air / movement in the SMC isn't going to cause the rear wheel to drag. But the SMC not releasing the rear brake will.
I had such a problem years ago - which turned out to be me applying too much rubber grease to the slider pins and boot. Smoking hot rear brake on the point of locking up solid.
Find what is causing it before you fix it.
You've had both calipers off. Take note of the chrome retainer clip into which the tab end of the brakes fit in the caliper bracket. The front and rear retainer clips are different, the rear one having a ridge, the front ones not having a ridge. If you have fitted the rear clip to the front left caliper bracket, then the front pads will not release after the brakes have been applied - this will casue the front left brake to drag, which will casue the rear brake to drag even more.
You've clearly worked on a lot of other bikes. The ST1300 is not like a lot of other bikes and often requires a different approach. Assume that you don't know how to fir a wheel; how to replace calipers and find what you need to know on the forums.
I have a lot of articles about wheels, brakes and SMC.
Here's a link to just mine - but read others as well.