There is none
As it is a method of communication, can it be taken as a language?
Nope. Thieves' Cant is a class feature, not a language.
is it mechanically equivalent to something
Nope. Thieves' Cant is a unique class feature.
Are there any other rule mechanics e.g. background, that could grant Thieves' Cant?
Nope. Neither standard backgrounds nor official (read AL-legal) class features can not grant Thieves' Cant to a character.
Lore-wise, Thieves' Cant is a steganography. It allows you to conceal a secret message in your convenient speech. It is based on a language, but is not a language by itself. A DM can allow Thieves' Cant as a custom background's feature. See the PHB page 125 "Customizing a background".