Does that mean the batteries are running out?

I just noticed when I switched on my Logitech connected to USB on the PC / laptop that it briefly flashed red. Could that mean that the batteries will give up soon?

Jo that's right

Hardly sounds like it, yes

The best thing to do is to have spare batteries ready

Why is there an obligation to enclose a manual for every device?
Everything is in there.

Here you are only going to get guesswork and I suspect that's what it means. The manufacturer gives you a better answer in the manual. I think he knows what he built.

We don't even know what you're talking about and maybe "she" charges via USB.

With some manufacturers you are not so sure whether they know what they have built when you read the manuals…

Unfortunately you're right again, but it's worth a try.