Those are features of AnkiDroid, and probably the desktop Anki also.
There is a daily review limit, and you can configure to see review cards before new cards. Anki does not tell you how much is overdue beyond the review limit.
If you're set on writing your own app, you will tend to overlook the configuration details of the original, though.
I think Anki is powerful and has a lot of configuration settings and add-ons to support new scenarios, but I think for a lot of average non-technical users, they may be overwhelmed by that and not interested in learning it. My goal was to write an app for those people (and for me).
I found with Anki that it was sometimes difficult to self report precisely how well I remembered something. It also added an extra cognitive step on each card to have to consider it, which over time was an annoyance.
I don't have any scientific proof that judging response time is better than self-reporting, but my thinking is self-reporting accuracy is low enough and forgetting curve is approximate enough for each card that in aggregate it doesn't make a huge difference. It would be interesting to have real scientific tests, but I think it would be difficult to set up.
I considered adding a way to self-report your score, but it didn't make the MVP and I'm really trying to target less technical users and not people who are already familiar with Anki. I might add it one day as an option since the underlying design of app can handle it.
If there's enough interest, I might try to port it to Android next year as a fun project.
I later wrote my own flashcard app[1] with spaced repetition and ended up hiding the details of what was overdue and instead just let you set up a daily goal of number of cards reviewed. When you do a lesson, it picks up the overdue cards first, but if there aren't any, it pulls in new cards instead.
It's funny because I originally thought telling you how many were due each day would be a great motivator (at least for me), but I'm finding I actually don't care. If you miss a few days, the cards still remain overdue, but when you return it doesn't feel bad.
I think for me, it's more important when learning to aim for the long-term commitment to it than to be perfect each day in your studies. If you aim for perfection, you end up not meeting your high standards and may end up quitting. Also, I think the "deadline" for when to review in spaced repetition isn't exactly accurate to the day or hour that something is due, so there's a little bit of malleability there, and I think that's okay.
[1] https://www.ussherpress.com/freshcards/