Thanks to everyone for your responses. Helpful to know others are seeing the problem.
@radtux - could you explain how to get the Blackberry keyboard? Is it the 'Keyboard for Blackberry' app? That didn't look quite right from the description.
@mgg - interesting that you see it on a Pixel. Everyone who has the problem on this thread so far has had a Moto so I had been thinking it was something Moto-specific.
I did report the issue to Fastmail (ticket 368552) - the agent said they couldn't reproduce on their phone and suggested reinstalling the app, which I just tried - no improvement. I will follow up and point them to these threads.
I am coming to the conclusion that I should just abandon the app and use the web interface or another mail app.
Getting frustrated with slow inbox loading and lack of offline access anyway....