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@allObjects
A good battery has about 1% self discharge. Battery Datasheets will tell you how the discharge goes with the duty cycle and duty current. e-ink displays have a heavy wake-up / start-up power consumption. If you run this once a day only, it should not be that a problem. For Puck I looked this for the CR3032 button cell up. Similar calculation have to be done for PICO.
How often do you plan to update e-ink display (a day)? If it is too often, a plain LCD could fare better... Yes the e-ink does use only power when rewriting the display (and it is always the whole display / page), but it is a 'lot' of power compared to an LCD which runs all the time but though on very very little power and 'much less' for update.
Just found the attached document on the Web. It may not give this or that battery, but a general understanding...
To come up with the capacity (mAh) matching your expectations regarding battery replacement intervals, estimate the duty cycle and current for the duty phase for a day.
Battery capacity is measured in mAh (Ah) - milli Ampere hours. For example: a battery that has 10mAh can sustain about 1mA for 10hrs. If you draw higher current than 1mA the capacity is less, in other words: 2mA will NOT give you 5hours... and 0.01mA may not give you 1000hrs (a 30 day month has 720 hrs, a year has 8760 hrs... don't want to be Mr. Obvious, just putting the numbers out...)
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