3–4 days on a 2000mAH battery means over 20mAH per hour. You say deep sleep uses <20μA, which would be under 0.1% of the total here, so we can call that rounding error and just focus on the time when it’s actively doing something. Assume it wakes up every hour, takes 12 seconds to connect, fetch and render, before returning to deep sleep. 20mAH in 12 seconds is 6 amps. I’m not familiar with the actual power consumption figures, but https://lastminuteengineers.com/esp32-sleep-modes-power-cons... suggests an ESP32 chip with everything on is using up to about 260mA, and I seem to recall hearing that e-ink displays used a few milliwatts, but it’s hard to find details. All up, my extremely rough estimates are coming to active consumption more like 300mA, not 6A—so more like three months than three days.
(I haven’t been careful with the voltages in these calculations, but my impression is that you’re looking at about 3.3–3.6V on the battery and ESP32 chip. I think the 300mA is probably fairly significantly on the high side, since most of the system won’t be in use for all of that nominal 12 seconds. But I caution you again that I’m not competent in this field; I’m just a layman that thinks the numbers didn’t add up.
While I’m talking: why do most of these things, especially the batteries, cite current figures rather than power figures? Is there a genuine reason, or is it some kind of historical mistake, or something else?)