I am sure the pads are not worn. Their thickness is 3.7 mm and a change is recommended below 3 mm. I don't think they are designed to be replaced after 2200 km on flat roads with sporadic mild braking. If so, then pro cyclists would need 2-3 pairs of pads for a long course in the mountains.
I have just investigated how disk brakes work and, indeed, the pistons compensate for pads wear. My brakes levers had a long course before they "bite" since they were new, but after that point the brake was strong. Maybe this is by design. I'm not happy with that, because when the "bite" started 5mm further away (for no apparent reason), the lever started to touch the handlebar.
I applied a workaround which made the brake fully functional as it was at the beginning: I forced the pistons to extend more by squeezing the lever after putting between the pads a spacer which is thinner than the rotor (1.5 mm versus 1.85mm). But I'm not comfortable with the solution, thus, I'll try a "bleeding". I'm curious to see the results, given the fact that the brake levers had a long course before the bite, even when the bike was new.