In 2025 Doctor Who episode "The Well," there is a character who communicates in both an oral language and a sign language, which made me wonder about how (and whether) the TARDIS translation circuit handles sign languages.
In the episode, we see the Doctor ably communicating with Aliss in what is presumably a sign language from 500,000 years in the future (obviously, "really" BSL, just as the actors are "really" speaking British English), which might suggest that it does translate sign languages. And why not, since it translates written and spoken texts, so visual and auditory communication both?
However, Belinda's comprehension seems a little more ambiguous, and she at least thinks that her words won't be translated. Not to mention that the Doctor just genuinely knowing a future sign language is completely plausible. I also seem to recall that Clara also did not understand what Cass was saying in "Before the Flood."
So does the TARDIS translate sign languages at all? If it does, can it do sign-to-oral or oral-to-sign, or does it only do same-type translation?