Looks intriguing, but do I have to take a picture every time I log in? That seems inconvenient.

I'm having trouble understanding what more this offers over a model more like TOTP/HOTP, where I can scan a QR code once from a site, then log in with it even if my phone doesn't have connectivity (which is a more common use case than you might think).

If I do have connectivity, why not just throw a prompt up on my phone asking "Hey can you verify that's you logging into our website?"

TOTP is an objectively worse UX - first you type in your username, then password, then open your phone, open the relevant app, read the code, and type in the code before it expires. With Keyri, you open the relevant app, tap a "scan" UI element, and point it at your screen. No typing, memorization, or race against the clock. Also, with TOTP, you're pulling out your phone and navigating to a specific app anyway, so I don't understand your UX objection. I'm also struggling to picture a situation in which a laptop or other device has connectivity but a phone does not. Presumably the laptop is on a WiFi network that the phone can also connect to. If the laptop is using some sort of satellite connection module, that module and/or laptop can fire up a hotspot. This connectivity problem would also arise in the push notification solution you propose in the next sentence.

Push notification solutions ("prompts") are defeatable using trivial man-in-the-middle phishing techniques. For example: https://github.com/kgretzky/evilginx2. Authenticator-initiated authentication solutions with two-way authentication like Keyri eliminate phishing.