Further details of the question. Sorry this is rather long but I've numbered it for clarity

1. Using Arduino IDE. I now have two identical circuits - Arduino MKR 1300 acting as simple passthrough using the program above, connected to HM-10 modules (sold as "genuine"). On the same or on separate PCs the behaviour is the same.
2. I confirmed connection by temporarily removing the HM-10s and cross-connecting TX and RX between the Arduinos (if you do this don't forget GND). Keypresses at one IDE were received at the other, in both directions. I then replaced the HM-10s.
3. I do AT+RENEW to reset both then leave one at ROLE0 (flash 1 per 2 seconds) and set the other to AT+ROLE1 (flash 1 per second); then to the latter AT+BAND(address of the former). Both leds then go steady (I assume paired). In this state neither responds to AT commands, but no keypresses at one are received at the other.
4. If I unpower the ROLE0, the ROLE1 led begins flashing 1 per second and repeatedly prints "SCANNING...SCANNING +INQ:no equipment" but ceases this and reconnects when the ROLE0 module is restored.
5. If I break the arrangement and instead use nRF52840 dongle with Nordic software it communicates in both directions to either HM-10 set to ROLE0.

I suspect that one or more of the settings in the HM-10s need to be changed. Any suggestion would be very welcome.