Thanks @msjcard - I don't believe it was any of those, and the cause is as per AN13539:
Note: OM-SE050ARD-E kit does not support ISO/IEC 14443-4-A.
My SE051H kit just arrived - and it all worked straight away.
Credit card indeed always failed to select applet, so connection was fine.
Native Linux driver for the reader did not make any difference.
I am not sure if there is such thing as "connectionless" mode for ISO 14443 without "4-A" - might well be. But I need something that could easily be integrated with mobile apps. Replacing SE050E with SE051H does not affect cost, so it is easier.