Ok, so. One of the races I'm making has a feature I'm not exactly sure how to balance. The idea is to have a feature where the race in question can quickly learn new languages, like a biological auto-translator. I'm not sure if I should make the effect permanent- I'd love to, but I'm pretty sure that'd break the game. I'd really appreciate feedback, and here's what I have so far:

Adaptive Linguistics. If you spend a long rest reading and listening to a language you don't know, you gain the ability to speak, read, and write that language fluently for 7 days. At the end of this time period, you forget the language and must spend another long rest hearing and reading it to gain this ability.

One problem I see with this out of the gate is that it's just straight-up annoying to have to redo it over and over again. Another possible and likely also broken fix would be this trait:

Auto-Translator. You can understand any spoken or written language. However, you cannot speak or write in a language you don't know.

Again- tell me if you have any suggestions! I'd love to hear them-

I honestly think the first one is great!

Unless your campaign is heavy on wanting language to be a barrier, recall that comprehend languages is only a first level spell, accessible to four different classes. Warlocks also get access to a second way to utilise equivalent translation skills at a fairly low level.  I would balance based on your campaign restraints since, RAW, languages are not that big of a barrier.

 I would just give them the ability cast Comprehend Languages once every Long Rest.   Easier to do, less record keeping, seems balanced with Elves and other such species that get a free 1st level spell

I don’t know why it would necessarily be game breaking. Languages can be critically important, all but useless, or anywhere in between. It going to depend on your campaign. If you include this ability, it seems like you are going to make them meaningful, or as a player, I’d be a bit annoyed at not getting any use from my racial ability. Making it permanent would kind of be like giving part of the linguist feat for free, or the warlock invocation eyes of the rune keeper, but temporarily could actually be kind of cool.

I don’t think the first one is annoying at all. You will pretty much hand wave the time spent doing it. Though you could say that as long as the character remains immersed in the language, they don’t need to keep re-learning it, and then the effects linger for seven days after they leave the area.

One thing I would specify is what to do with codes. Or things like thieves cant which isn’t quite a language, but a way to use a language. I’d just make it clear that understanding the language isn’t the same as understanding secret meanings embedded in what they read/hear.

And that a symbol might not necessarily be a language. For example, most people nowadays know a second meaning for something like an eggplant or peach emoji. Is that a language? Would the ability let people understand that? Or just be confused at this discussion of wet eggplants after asking if some is awake?

With languages...it is as broken as you make it to be in the campaign. If you have a whole bunch of puzzles with amazing rewards for solving them that have their solutions written nearby in various languages, yes, it will be a very broken feature.

My adventures have never had that kind of circumstance. In the seven adventures I've done, having an extra language has been a positive trait a grand total of twice (a single instance each in two of the adventures), and only once was it advantageous.

It should also be noted that Comprehend Languages is a ritual 1st level spell that let's the player understand any language. That means for Wizards, if they choose this spell, they can cast it as a ritual, so it doesn't necessarily even take a slot or even space on their prepared spell list with no material cost either (assuming they have an Arcane Focus or already have soot and salt to hand), and it just takes 10 minutes to cast in that manner.

That is much better (in a mechanical sense) than yournfeature, and my Genasi gets a bunch of spells, including 2nd level spell Flame Blade for free. So your feature really isn't over powered.

I wouldn't consider having to renew the language once a week annoying. Unless you're having to do multiple language all the time...it's actually getting you to engage with the mechanic more, making it a better one.

It's fine, honestly.

I'd say instead of putting the time limit on it, just turn it into an always-on feature, but only allow the player to know one language at a time. I think this is how I would write it...

Language Savant: At the end of a Long Rest, you may choose one Language which you are not already Proficient with and become fully fluent in that language. You remain fluent in this language until you use this feature to become proficient in a different language.

How that happens in roleplay terms is entirely a flavor thing... perhaps it's flavored as the player actively studying the language during the night, or it's a purely psychic or magical effect. It doesn't really matter... the important part is that this version functions basically how the player would ultimately use the feature anyway (since they'd just refresh it each 7 days, unless they're swapping languages).