I do get tootsuite => toute de suite i.e. a sense of immediacy, the present moment, with greater impact for being a bilingual pun. Along with that, the onomatopoeic elephant.
Cynical take: notwithstanding the denial in the PR, that original author knew the scatological allusion, and that it has parochial scope, i.e. they actively intended to annoy Americans, and in particular those with a prim streak.
Beans, beans, the magical fruit, the more you eat, the more you toot.
That cemented the association with farts, but 'toot' as in 'toot your own horn' (idiom for self-promotion), or even just literally tooting a horn, are also strong associations. So it's not exclusively, or primarily, a word for farts to my ears – but that's one of the top few potential meanings.
The GP form I have never encountered before, and by my assessment falls short in pedagogical qualities.
That's why they make you toot.
It's not intended as smack talk asserting "My variation is better than yours!" (Throws down gloves.)
Sometimes, it's nigh impossible to readily come up with the wording that captures the myriad thoughts flitting about my mind and account for all possible social bits and potential misinterpretations. And I comment anyway, knowing it's likely to go sideways cuz hoomans.
Sometimes that last is funnier, though usually only to the person doing it.
That makes total sense.
Regular correspondents to this forum may also encounter Java beans, but be warned that their palatability is disputed, and ungoverned use, particularly in their enterprise form, can lead to buildup of toxic and irrevocable technical debt.