What does the ‘Special Feature’ teddy bear sticker mean on some games for Sears/Atari 2600

I doubt it. Breakout on the Atari 2600 used analogue paddle controllers, which means the input from the controller itself is unlimited. There'd have to be code in the game to interpolate a slower speed and it's hard to see why the developers would want to allocate some of the very limited memory available for 2600 games on something like this. It also would imply that the authors of the paper cheated and modified the game to remove that hypothetical code. Given their goal isn't to beat Breakout but have a program learn to play Breakout cheating like this would be self defeating. If anything they should be adding code to limit the paddle speed and accuracy to what would be physically possible for a human.

I also vaguely remember paddle games of the era not being speed limited, but I don't think I ever played Atari 2600 Breakout. I don't think speed limiting became a thing until digital controls starting being used to for these games, which are inherently limited to whatever speed the developer chooses.

If you can find an Atari Hangman or Surround cartridge, you may want to see what happens when you play those. I would not expect that the memory within a 2600's RIOT (RAM+I/O+Timer) chip would be likely to go bad, but if those games exhibit "stuck" pixels, bad memory would be the only likely explanation. I suggest those games in particular because they use a significant portion of the system's RAM to display a bitmap, and any problems in those portions of the RAM would manifest themselves as stuck pixels without any other side-effects.