We can see a badge for found lab caches, so it seems BadgeGen is counting in also Lab caches. Then, on the other hand for the BadgeGen belt points, there is e.g. one item scoring 2 points per cache type hidden. In here, I do not see a hidden lab (adventure lab) would have an impact, so it seems they are not included. For the sake of consistency, it would be good to have lab caches included here as well (or then totally excluded).