That battery should last 10 years due to the very shallow cycling we did on it. It only gets charged to 3.9v max, the usable capacity is less than half the design capacity to extend the life.

Is Voc listed at 37v? That's a bit high to be honest. It's possible you have no issues with your battery but you're hitting overvoltage lockout on the buck preventing any charging from happening. Did anything change with your furnace? I'd expect a lower number from a 24v transformer (I see 21v on mine, which is on the low side, but above 35v is also unusual).

Nest DVT serial number 1 still going strong on my wall (and I only have RH/W wires, no C).