I'm currently learning Japanese and what I've found is most apps designed around helping you learn focus around memorization of words out of context, and often the definitions provided are wrong, or the words antiquated.
I haven't found an app that revolves around reading words in the context of example sentences, or a narrative. I find this to be the best way to learn a language.
I totally agree with you on context. Something that has worked for me is to add the Core10k(http://rtkwiki.koohii.com/wiki/Core_10k and the Core6k decks to Anki and then when I bump into a new word I want to learn, I search for it on these decks and move the corresponding cards to my main study deck. These decks have the words in the context of one whole sentence including audio and images. Also, I only add words to my main study deck that I have seen in a real Japanese text.
That is not enough though and that problem you are describing is the reason I am developing Koipun Reader(https://www.koipun.com/reader/). My goal for Koipun Reader is to help intermediate level learners go through any arbitrary Japanese text and give them the ability to save words they want to learn, so that they can review them later within the same context of the text they read. I only have preview version of the app right now, but I will release an MVP in a month.
Everything is in context, it has a practice portion for things you needed help on, you can make lists of vocab, it tests for kanji writing as well as reading, and the zatsugaku challenge has lots of interesting things going on.
I haven't found any other tool to be even in the same league
Ah, I learned first going to normal classes and for me the experience was the exact opposite. Now I'm doing a lot of memorization, since it's one of the pillars for learning a language that I was lacking. I recommend trying to do both at the same time, but the good thing about learning a lot of vocabulary and some grammar is that you can start reading on your own and then learn while having fun. I am reading Yotsubato for example, which is widely recommended for beginners.
I think if you already know to read/know the basics, learning vocab is fine. That's why SAT prep is a lot of vocab memorization, but even then you'd have to know how the word is used in a sentence.
Learning from scratch, I think vocab is better memorized in context.
Not sure if they have an app, but the "minna no nihongo" books I had at university in Japan when I was there for a semester (10+ years ago) taught with contextual scenarios, as you said.
I haven't found an app that revolves around reading words in the context of example sentences, or a narrative. I find this to be the best way to learn a language.