I have been using https://neuracache.com for spaced repetition; it pulls cards out of Logseq and has a nicer native iOS app built specifically for spaced repetition with push notification reminders, etc.
However, I’d love an app that still uses Logseq to store my “state” (i.e. which cards I have memorized, which ones I have not).
Is this possible today? Or can cards be “pulled” from Logseq without any way to “push” state changes back?
Welcome to the forum @irace! 
If you use Anki, there is a Logseq plugin called Logseq Anki Sync that achieves this. It has bi-directional functionality, meaning that you can push cards to Anki to Logseq and vice versa.
The plugin is available from the Logseq Marketplace (within Logseq, click ... in the top bar and then Plugins). You can find more info about the plugin here: https://github.com/debanjandhar12/logseq-anki-sync
Hi, I use Neuracache too, very convenient.
I did some tests and I found the state of cards is stored in a dedicated file: graph/logseq/srs-of-matrix.edn
Neuracache should be able to read/write that file to get the state synced, but I can’t find any documentation on how to interpret that file (it’s just made of numbers in {} brackets).
Months ago I contacted the Neuracache developer asking to fix Logseq import and he was very kind and responsive, it fixed it in a few days and indeed we can now use Neuracache+Logseq.
I suggest you to contact Neuracache developer and eventually ask Logseq developers for some documentation about that file.
About Anki plugin, I did some tests before discovering Neuracache and it seems it just sync Logseq → Anki and no state sync, but I may be wrong and was not able to set it up.
Thanks for doing this digging and providing an answer! I’m checking internally if there is documentation about the structure of this file, or if we can create it.