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. Spells like Comprehend Languages do not allow you to understand Thieves' Cant.
Are there any other rule mechanics e.g. background, that could grant Thieves' Cant?
Nope. With the DM's approval, only custom backgrounds or homebrewed class archetypes can give Thieves' Cant. There are no 'official' (AL-legal) ways to get this feature other than taking a level in Rogue.
Lore-wise, Thieves' Cant is a steganography. It allows you to conceal a secret message in your convenient speech. It is the skill to hide secret messages in whatever language you are currently speaking (thanks @guildsbounty).
A DM can allow Thieves' Cant as a custom background feature. See the PHB page 125 "Customizing a background":
If you can't find a feature that matches your desired background, work with your DM to create one