having dealt with race bikes for 20 or so years, lots of crashes and rebuilds, a common pilot complaint is bike pulling one way or another.
Assuming frame and swingarm are straight (aka not crash victim)
First thing.. is your windscreen aligned? is one side back further in a way that would cause a boat sail effect?
Check the triple clamp
1) first check that there is no bearing play in the headstock, any bearing play will cause the triple to "lean" slightly and can cause vertical alignment issues. you'd normally get head shake (speed wobble) at speed if the top bearing goes but if the bottom bearing is bad, i've had riders at 100+mph with no headshake fighting to keep going in a straight line and bottom bearing was bad.
2) undo the fork clamps and pull the bolts entirely. Make sure the mating halves of the clamp (that you just pulled the bolt from) actually line up on their own and not have to be lined up by force. if they are out of alignment, you can try heat bend to align, but honestly you may feel more confident with just replacing that clamp.
3) make sure the 2 fork bodies are at the same unloaded length (they can be short valved accidentally if they are rebuilt, we do it sometimes to lower the bike or decrease travel). you may need to accommodate for this difference in unsprung length to make sure the longer fork isn't causing slight sprung torsion on one side.. (this would be a theory test, solution would be to rebuild the shock valves to full extend to same length.
4) if things check out above, reinstall forks and make sure they are same height in the triple clamps. I generally just use the depth gauge on my verniers, but they don't have to be laser precise, as too many other factors will cancel out their precision.
5) make sure the top and bottom parts of the triple tree are aligned.. generally though you'd be fighting the bike to centre the bars if they were out of alignment, but i've seen so many off just enough to be noticeable by the rider, but not noticeable on the paddock stands or when you give the old eyeball from the front.
6) check front axle. pull it out, make sure its straight. check bearings while you are there. a small bend you won't notice while pulling through the inner bearing race, a big bend.. well you aren't getting the axle out. a small bend is enough to toss alignment out of spec, and considering this bolt is thread captured, it'll always land in the same bent spot when you reinstall, so (like some bikes i've worked on) you can't simply spin the axle and see if the behaviour changes. More than likely though, if its pulls out smooth, its not your issue.
Move to the back end
1) swingarm bolt, pull it out, clean it up, check for true, more importantly, is it worn flat in any spots, if its off just a bit it'll move your rear wheel out of alignment just enough to make it pull .. it actually doesn't take much of a bend to cause it to drift. you'd likely notice odd tire wear, that seems to be off centre just a bit as the tire malforms to adjust to the fight in alignment.
2) rear axle.. check if its true.. given the Super Tenere is captured on both ends permanently (unlike when you have a chain and can do left/right tensioners), the only thing that could be bad is the axle
3) check bearings in there while you are at it.. never hurts if you've got it apart.
if all that checks out, then realistically it could be a big combination of little things that are doing it.. it sounds like you've tried doing external factor changes, but have you considered your riding position? Is your butt centred on the seat? does your body relax in a method that puts weight off centre.. me for instance, a bigger boy and the sufferer of about 10 broken ribs over my racing career, when relaxed, my left shoulder slumps down further than right, which pushes my right bar out. if i let go of the bars, my body does seem to naturally counterbalance in the seating position and sure enough i can stop it if I center up and straighten my back. If I'm unsure, I ask a friend to take for a rip and ask if im imagining things. sample set of 2 is better than 1
about all i can think of.. my S10 runs dead straight otherwise, but i did a full teardown when I bought it (used) to give it good once over and cleaning as a winter project, and I did notice that tolerances aren't super tight for some things, where routine maintenance is supposed to catch them as problems.