In your au's, did Anakin program Amatakka into C3PO when he built him? Because I kind of want to see Luke's wft reaction when the protocol droid from the wealthy "Core-worlder" planet of Alderaan, of the Royal household no less, suddenly responds to Luke in the secret slave only language. Or even more, Threepio quietly but unthinkingly translating something Luke is saying to Leia, and providing cultural context, unintentionally being a bridge to the culture for her.
Anakin did program Threepio to speak Amatakka, yes. But Threepio underwent a full memory wipe and factory reset at the end of ROTS, which means that OT Threepio not only doesn’t speak Amatakka, but isn’t even aware that it’s a language that exists.
Threepio is physically identical to a number of other protocol droids we see, which likely means that Anakin didn’t build him from scratch, but rather refurbished an existing protocol droid. My personal headcanon is that he found the shell of a defunct protocol droid in Watto’s junk shop and rebuilt him (made him stronger, faster, better...).
Who Threepio was before Anakin rebuilt him will probably never be known. I don’t think he has any memory of his previous existence, and it may not have been much, as he was likely regularly memory wiped in his previous life. (That seems to be common practice with droids in the GFFA, and maybe especially with droids who are involved with potentially sensitive work, as protocol droids would be.)
The droid that Anakin brought to life, though, was an fully realized individual. Shmi and Anakin allowed and encouraged Threepio to define himself, and they certainly never would have considered wiping his memory. He spoke Amatakka with them on Tatooine, and retained that knowledge after he went to live with Padme. (In fact, Padme may have learned as much Amatakka from Threepio as she did from Anakin, and possibly more, since she saw Threepio every day.)
When Bail Organa had Threepio’s memory wiped at the end of ROTS, he was given a full factory reset, which meant that he retained his knowledge of every language and mode of communication he’d originally been programmed with...but not Amatakka. Amatakka is a secret language, and therefore not part of any standard programming package. It’s very existence is secret, so Threepio isn’t even aware that it’s something he’s missing.
I’d like to think that, at some point either during or after the OT, Luke programmed Threepio to speak Amatakka. But there’s no way for Threepio to know that’s something he once knew and lost, and, unless Anakin’s ghost told Luke, there’s no way for Luke to know Threepio once spoke his language.
And knowing a language doesn’t necessarily mean knowing all the cultural context that goes with it. If Luke does program Threepio with Amatakka, that won’t mean Threepio suddenly regains his memories of his time with Shmi and Anakin and the culture of the Quarters in which he had his formative, now lost, years. Those memories are gone, and there is no way to recover them. Whatever knowledge Threepio has about Amavikka culture in the OT and beyond will be filtered through Luke’s knowledge, and not through the lens of the Mos Espa slave quarters.
