Xperia series from my perspective. I've tried a lot of phones, but the Xperia series seems to have the best most consistent read at the moment. (They all use the same little square antenna, it's a good match.)
That was it! The culprit seemed to be a rather poorly written app from our city's public transit company, that is supposed to use NFC to read transit card info, but actually never works. The keyboard issue appears to be gone with this app removed.
Thanks for the tip! I'd never have guessed it, the app wasn't active or even open as a background process.
No surprise it doesn't work with Apple. They would want to sell you an iRing at three times the price, then claim that it's new groundbreaking technology invented by them, like, err, contactless charging...