I recently began using tappedout.net to keep track of my cards and I couldn't help but wonder if there was an Android app that fulfilled the same purpose. Might you assist me in my search?
Yes, there is. I was looking into how I could catalogue my own collection at a decent pace, and manually typing in card names just wasn't going to cut it. I have a Windows + Android device, so I went searching too.
Since you're using TappedOut, it would be remiss of me to not mention that TappedOut has its own Android app: the TappedOut MTG Companion which includes a "visual collection updater": in theory, it lets you lay out your cards nice and neatly, photograph several of them at once, then add them to a collection. I say "in theory" because I've not yet been able to use it successfully — I've just gotten an error when I try.
The app I went with to scan my own collection was Delver Lens. Out of every Android app, it is the only one that scans cards and lets me output the list to TappedOut. (In fact, it's even got a custom export format prepared just for TappedOut!) It does one-by-one card scanning, and it's a little finnicky but easy enough to get the hang of. Overall I was able to catalogue ~140 cards in a few minutes using this, then export them to my TappedOut inventory just fine.
All Windows and other Android applications I'd found didn't give me an exportable list, or only existed to check market prices. Accordingly, I have zero other apps to mention that perform this purpose.
I have no affiliation with any of the products I've mentioned beyond being a ordinary user, and I do not gain anything from recommending them.