I have used this tool on many different topics. It helped me through one test at school years ago. Now I use it for general/random topics of all sorts that seem interesting to me.
I opened the first Google link I found about f-droid and anki (https://f-droid.org/packages/com.ichi2.anki/). The app doesn't have the same app image as the Anki I talk about (there are other versions done by someone else)so I don't know, is this the same app. I did a search in that website for Anki but I didn't find an equivalent for it in there.
Oh! Login at ankiweb.net?
I didn't know about that limitation. I have an account so I missed that.
Well - if going after already-existing data is not your thing because of that limitation going on, I'd still suggest to give the app itself a try 👍 (creating your own cards/decks)