It is normal for the pistons to look absolutely filthy. They get covered in crud kicked up from the road, and it can harden.
But they will normally clean up well to a shiny polished surface with a hint of bronze.
Post photos, it may help us to spot something.
Remove the pads - only pad pin removal is required for this, the pads will slide out easily if you rotate the back wheel backwards.
It is fiddly getting in there to clean the pistons, but much easier if you can take the caliper off the caliper bracket.
But it is possible to do it without, but you are working blind. A flat bootlace. soaked in brake fluid can be wrapped around each piston in turn and cleaned like drying your back with a towel. But it is difficult to see how effective this has been.
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You will see a hex headed bolt underneath the caliper. DO NOT REMOVE IT. This is one of the slider pins.
Instead you need to undo the much larger caliper bracket stopper bolt, and take the caliper and bracket off the axle. This means swinging both silencers down - the right one to take the axle out by a few inches, the right one to access the stopper bolt. It is a good idea to put the bike on the centrestand which is on a half inch piece of plywood. Ive had one st1300 where this was necessary to allow the right exhaust to swing down far enough to allow the axle to be pushed out partially. My current ST1300 does not need me to use the plywood. You may need help pulling the bike back to get it on the centre stand. Its much harder with the plywood.
The left silencer needs to swing down a bit to get the stopper bolt out. This has a large hex head 14mm I think, and the bolt is screwed into the top if the swing arm - the two brake hoses curve over the top of the casting where the bolt fits.
With axle pulled pulled out far enough , one end of the bracket is free to remove, with the stopper bolt removed, the other end is free as well. The bracket and caliper can be lifted over the brake disc and then separated. The bracket slides off the two slider pins - but be careful with the brake hoses - they should not be put under any strain.
The caliper can be turned upside down - the hoses are long enough to allow this. Find a piece of wood that will fit in the caliper in front of the pistons with a mm or two clear space. Gently press the brake pedal until all 3 pistons meet the piece of wood. Do not allow the wood to slip out - it is there to stop the pistons moving out too far. You are trying to move all 3 pistons out by just a mm or so. Take the wood out and do not touch the brake pedal again.
Now you can clean the pistons much more easily. Toothbrush and brake fluid, followed by flat bootlace and brake fluid. I keep the sewn hems from worn out cotton towels, teatowels, jeans - any old cotton stuff that gets discarded into the 'these will do for rags' bin in the garage.
Inspect the pistons for rough patches, corrosion or pitting, where the hardened shiny surface coating has started to lift or has come off. Even a small defect means that the piston needs to be replaced, as the piston seals will then not prevent fluid from getting out and braking will eventually fail.
I smear the exposed part if the nice shiny pistons with red rubber grease. This is specially made for hydraulic seals. Normal petroleum based grease causes the seals inside the caliper to swell cinsiderably and should not be used. Ive heard people say that this is a magnet fir muck. No it isn't. The rear caliper and bracket is in the direct line of fire from crud kicked up off the road by the front wheel.
People say that the muck sticks to the grease. This is true, but it also doeas a pretty good job of sticking to the polished surface without the grease being there. Its fine particles in the rainwater which then sets like concrete. But the rubber grease helps to protect the surface of the piston, and it is easy to clean off. The pistons MUST be cleaned of muck and grease before they are pushed in to accommodate the new pads.
Clean the slide pins, and clean out the muck and grease from the holes - 1 in the caliper, one in the bracket - check bith rubber boots.
Smear both caliper pins with red rubber grease or equivalent stuff suitable fir hydraulic seals. A thin visible coat.
Fit the two slider pins into the matching rubber boots. One pin is longer than the ither, which makes it easy to locate that one first. Check the pad spring is in place and is the right way round - wider strip nearest the pistons. Use the piece of wood and insert in frint of all 3 pistons. Twist it slightly to push in all 3 pistons by the couple of mm that you moved them out.
Check the chrome retaining clip is in place in the caliper (ridged one for the rear, flat for the front).
Wipe the grease off the rim of the piston, so that you do not get grease on the brake disk later.
Put the caliper bracket in place and gently slide the axle part way to support it.
Clean the stopper bolt. Boliing water will help remove the old thread lock. Clean the threads. Molypaste the smooth shaft of the bolt. Apply thread lock to the threads. Insert it into position and screw it in finger tight. Check that it is located properly through the elingated hole in the caliper bracket. You can see this through the rear wheel spokes from the right hand side, assuming you took the panniers off. The end of the bolt has a mark like a screwdriver slot in the end. You MUST see the end if the bolt properly located in that slightly oval shaped hole.
Push the axle in all of the way.
Grab a handful of caliper bracket. Push it in towards the wheel - careful, try not to push it so far that the pistons touch the brake disc. Let go. It should stay there. Pull it out as far as you can. It should move easily and freely with only a little effort. Let go. It should stay there. If you used too much grease on the slider pins, then it is possible that the movement will create too much air pressure or vaccuum and the caliper will move back. This will cause sime brake drag.
All Ok ?
TIGHTEN THE STOPPER BOLT. Its a hefty load 69Nm I think, but please always check for yourself.
Tighten the axle. Spin the wheel and clean up the brake disc with alcohol. Tighten the axle bolt. Even heftier - 108Nm - I think.
Clean the pad pin, nice and smooth and shiny and apply a smear of grease - molypaste would do or copper grease. Refit the pads. I use ceratec on the back of the pads. Manual doesn't call for anything.
Check the pads are properly located in the chrome retaining clip at the front of each bracket. Easy to see on the left with the exhaust out of the way. Look through the back wheel from the other side for the right.
These checks are important. You cannot see where the end of pad is going when you insert it, you can only feel. I have seen the inner pad on one bike where the forward end had dropped, and missed the clip completely. the end of the pad was resting on the hub. Eventually it would have worn through, slicing the left hand side of the hub away from the right.
Slow, methodical, check.
All of this is a lot of effort - but a lot easier if it is done when you have new tyres fitted. I remove my wheels and take them to the dealer and my brakes get done while the wheel is off. For me, this is every 5000 miles. And I often check partway through their life.
Dealers tend to take shotrcuts, liberties and little care - in my experience of having them do work. If I need them to do things as I dont have the skills or the tools, then I take the fairing off and ride it in naked - the bike, not me. The few times I have left the fairing on, it has never once been fitted properly. And these were Honda Dealers.
