It looks good. But it's weird the github has almost 1K stars, while it has only 1K+ download on google play[1]. So i'd continue to recommend Aegis, unless they use Apple device.
Like I previously said, Ente Auth was created due the developers of Ente Photos having a
"(...) had a hard time finding a place to preserve our two-factor secrets.". The main focos of the Ente team seems to be their main application so I do not know if Ente Auth will get the same amount of development that their main application has. They did released a version 2.0 within a year after the first version was released[2], so who knows if this will develop in one full fledged project. Note the note at the end though:
Our source of revenue is our Photos app, and Auth continues to be a labor of love. So we hope you'll enjoy these goodies 💚
Do note, however, that they also talk about the possibility of this becoming a paid service[1]. For now it remains free to use.
[1]
https://ente.io/blog/auth/[2]
https://ente.io/blog/auth-v2/