While there is not any official reply on an FAQ or the Rulebook, I’d say they are not counted.
The causes are primarily what you already listed. The guidelines explicitly say they are not a part of your provide, in addition to which you can’t use these tokens for the rest.
[…] To fill a Canteen, place a gained that flip onto the Canteen as an alternative of into your provide and carry out the Canteen’s motion. You can have any variety of Canteens, and any variety of your Canteens might be crammed on a flip should you achieve a number of. Once a Canteen is crammed, the stays on it till the tip of the Season and can’t be used some other approach.
If the canteen water was topic to the 12 restrict, saying “Any variety of your canteens might be crammed” wouldn’t be true; the restrict could be as much as 12. This is a stretch, however I really feel like this rule would’ve been worded in a different way if it was topic to the restrict, one thing like “and any variety of your canteens might be crammed on a flip, as much as the utmost carrying restrict, should you achieve a number of.”