See what? Is this another example of Swahili leaving out the direct object that would be required in English for a transitive verb?
(I'm guessing it doesn't mean "We will decide / find out later".)
It's just another example of the English translation not being up to scratch. It means "We will see each other later." The normal English translation of this would be "(I'll) see you later!"
kuona = to see
ana = to see
But wouldn't the question then say "Tutaonana"?
Here, they didn't mention "each other" in the Swahili ("Tutaona").
Well, it doesn't mention "us", only "we". (Also, that wouldn't be a grammatically logical sentence in English. It would have to be "we will see them" or "they will see us" or "we will see each other".)
Maybe we just have to take it literally: "We will see later". What we will see is unknown, both in this Swahili example and in the given translation, so they do in fact match each other.
Can any native Swahili speakers explain whether this has some other meaning (as in "We hope to have a day off soon but we will see", or something like that)?
That is an outdated rule (if you mean that "we will" is incorrect).
See this usage explanation from the Oxford dictionary entry for "shall":
In practice, however, shall and will are today used more or less interchangeably in statements (though not in questions). Given that the forms are frequently contracted (we'll, she'll, etc.) there is often no need to make a choice between shall and will, another factor no doubt instrumental in weakening the distinction. The interchangeable use of shall and will is now part of standard British and US English.