The  trick is to impersonate what the other program does, in ps,

flatten a texture- double the image's canvas size, select the image area. Copy ,

paste a coppy on each side and ech corner (or drag it over to the white area )

it wont be seamless but the trick might be to flip things on an axis

or for even more Whacked out idea  create aspecific size tile and create a double brush.  say you have a 400x400 tile  if you have two exact same brush heads (acting as one actual brush) with thier centre's 400 pixels apart you can paint over seams , you may need a vertical and horisontal versions (?)

the image i provide is a single brush you can try as experiment.