I thought I'd pop this up. It's mostly common sense, but it took me a while to reach a rather basic conclusion:

When a device is updating lots, you want a larger, cheaper battery.
When it's updating less often, you can get away with a smaller device.

Previously, all the zigbee sensors I bought were coin cell. Nice and small, comes with the battery, works straight away.

The first was a magnetic window sensor. Tiny device, and 2 years later, still running on the battery it came with. It only transmits when there is a state change, efficient, good plan.

Next up, a fleet of Sonoff ZB02 temperature sensors.
Tiny things, easy to hide around. They update every few minutes. After a year or so, the batteries started to go. 2032 cells aren't exactly cheap, so I bought the budget brand, paying about 50p/cell.
However, the replacement cells last about 6 months.
Better quality cells cost about £1, and last a year.

This isn't ideal, as they're a bit of a pain to prise open, and not exactly cheap. Since I'd seen people online discussing modifications to add AA/AAA support, I thought I'd compare the capacity.

A 2032 generally has between 100 and 400MAh, depending on the brand.
An AAA has around 1000MAh.
And two are required to reach the 3v of a coin cell. Depending on the quality of the button cell being replaced, that's 3-10x the capacity. Price wise, it's the same for me, £1 for two decent AAAs.

So based on that, I switched things up. Tuya sell sensors that run on AAAs.
And so far, the new temperature sensors are lasting much better.
They're a little larger, granted, but it's a good trade off.

Of course, I didn't reflect about what I'd learned, and bought some new window sensors that take AAAs. It was only after setting them up, that I realised they're big, and that the batteries will last until the heat death of the universe. Oh well.