This depends largely on the transmission conditions between the router and the 440. I use 3 of them to control radiator thermostats (router in the basement, 3 floors above). The buttons are not used. With one 440, I had to replace the batteries after 1 year.

After 3 months of use 90% displayed with original battery.

What is "infrequent use" of the push-buttons?
Push-buttons are in use 24/7 in the DECT radio network. Battery life also depends on the quality of the batteries and the environmental conditions.
All in all: I think the batteries should do their job comfortably for 1-2 years. The battery status in % can be queried permanently, below a critical value, which can be set, a mail is also sent as soon as desired. Battery life therefore plays a subordinate role overall.

I've had the original batteries in it for 11 months. The e-paper display needs almost no power to operate. The battery level is still indicated as 50%.

I have several 440s in my holiday home. Due to Corona, I haven't been there for over a year. But I still get reliable temperature reports.