How do I know my Honeywell valve is working?

Hi! First time poster.

Recently moved into a new house and trying to figure out the heating system, learning as I go. I'm a complete newbie when it comes to heating systems.

I've identified two valves (which appears to be called a S-plan system). One is a Drayton. When I turn heating off and on from the programmer, I can see the little lever on top of that valve move. Also, if I feel the pipes above and below the valve, they're hot, suggesting hot water is flowing through.

But I'm confused by the other valve. It's a Honeywell V4043H. If I turn hot water on and off from the programmer, I don't see the lever on top move. Should it? It remains in the position named AUTO. The other position is labeled MAN OPEN. The fact that it's labeled "AUTO" and not "OFF" makes me think perhaps it shouldn't move. But there's also the fact that the pipe below the valve is not very warm even though the programmer light indicates that hot water is on.

One theory is that the hot water tank is already hot enough according to its own thermostat, which prevents the valve from opening even though the programmer says it may do. I guess one way to confirm that would be to leave the hot water off for a while, then turn it on and see if the lever shifts or the pipe becomes warmer.

We've been taking showers and baths and the hot water was fine then, so unless something suddenly changed, it does seem operational. Since the last shower or bath we've self-installed a Nest Thermostat, but we only replaced the old Salus room thermostat using the same wires, which only involved heating and not hot water, so I doubt that has any bearing. One reason I'm trying to make sense of the system is to make the Nest control the hot water, too.

Sorry for the rambling – does any of this make sense? The main thing I'm looking for here is more details on how the Honeywell valve is supposed to behave in relation to the programmer, and whether the things I'm seeing indicate something may be broken or if it's to be expected.