There are a few places where the hints lie to you
. I’ve noticed this with some blanks where we are supposed to give the word for a specific relative. Then when we provide the word, the hint asks for a “more formal” word when in fact it is looking for a less formal word. I’ve found this with 祖母 and あに and there may be a few other instances as well.
I just took a look and the hints all appear correctly.
For example if you type おにいさん for the あに vocab cards, it will tell you it is look for something more casual (あに being more casual). The inverse happens for 祖母 where if you type おばあさん it will ask for more formal (祖母 being more formal/polite).
Hmmm I would expect おばあさん to be more formal than そば. It start with お。But I looked a little more into it and yes you are correct. Odd.
It makes you wonder why the word おばあさん even exists. If the formal word is shorter and simpler, why would you want a longer and more complicated word for casual speech?
Word length is not the sole determiner for formality register. It seems to me that words that comprise of multiple kanji with on-yomi readings give a more formal register. Similar to 忙しい and 多忙. The shorter one is much more formal. In your case, おばあさん is more like Grandma, 祖母 is more grandmother. I don’t think I have ever heard anyone refer to their grandmother as 祖母.
TIL this is more formal… I am embarrassed
by the way to expand on the discussion:
kango 漢語 (words derived from chinese) tend to be more formal/technical in general, and are usually kanji compounds, which I guess sometimes makes them shorter than the 和語 counterpart. Though not all kanji compounds are kango, so be careful. Also kango isnt alwaaaays the more formal word, but it often is.
Examples:
遅くなる ーー> 遅刻する
おばあさん ーー> 祖母
始まる ーー> 開始する
kango is used a lot in keigo in particular, like 利用 instead of 使う
Feels like this is similar to how words in English that are derived from French are typically the more “high brow” (kind of) words for things. Only the rich and educated spoke “French” because they were the Norman conquerors. The best example I can remember is cow (comes from “German”) which is what peasants would have used and because it would be rarer for them to eat cows, English naturally leaned towards beef to refer to foodified cows because the rich (Norman) people would have been eating them a lot more frequently. In ancient Japanese society, only the rich were able to have the resources to learn the new trendy words and writing system coming from China and also have the time to bother. I’m notably bad at knowing kunyomi and onyomi, but I’m betting the kanji compounds are more likely to be onyomi and the single kanji ones are more like to be kunyomi.
(fan theory - this blog post is not sponsored by the history of the Japanese language)
There may also be a difference when talking directly to your grandmother vs when talking to others about her. 祖母 being the more formal, but may sound “cold” when talking directly to おばあさん.
An English parallel could be talking to your dad and calling him “father” directly? That may sound cold in general.
Let me know if I’m wrong
Sorry in advance if this is a bit confusing or off-target, but I think the confusion here is what “formal” exactly means, as it is not specifically tied to the register of the word.
お父さん is a more “formal” word than 父 in the sense that the former is an honorific form, but when referring to your OWN father, お父さん sounds more familiar, while 父 sounds a bit blind and clinical.
On the contrary, if you are speaking to another people, the uses of お父さん “elevates” you father and this carries an honorific nuance.
TL;DR there are “honorific/polite/humble/etc.” forms for words and phrases in Japanese, but these also need to be considered in the context of speaker/audience.
I think bunpro should probably use hints like “more humble” or “more honorific” rather than formal in cases like these where the formality is dictated by relationships? Because as you say, it’s confusing about what “formal” actually means in these discussions.
Just to add on to what @John-Bunpro has already said here, we use the hints formal and polite in very specific ways on the app, and try as hard as we can to distinguish between those two as much as possible. Basically @cafelatte hit the mark 100% when she said -
This is the key. Polite language is language that you use to make your conversation partner feel better or in some cases even just to sound cuter! However, formal applies to language that would be found in books, is used in speeches, official documents or addresses. 9 out of 10 times, the kanji compound will be the one that sits in the latter.
Thank you but I’m a woman 

(Not super important but I feel the urge to call out implicit gender bias when I see it!)
My bad! 
(Bunpro hire me for equity and diversity) (jk)
No soup for you