Help with Esp32 Days Since Last Incident Board

Hello!
So I would like to make sure that my current plan for my project will work and not explode so any guidance on how it could be better or if I am trying to do something impossible would be greatly appreciated.

I am in the process of planning out a Days Since Incident board using an E Ink screen a generic esp32 and a Battery Shield to power it with a 3400mah battery.

My plan is to have the esp32 go into deepsleep after storing the previous Days Since Incident (going to call it DSI) in the RTC memory and then put it to sleep for 24 hours (Is there a way to make it wake up at midnight or can it only use a timer?) and then wake up check with NTP to see if it is around midnight then get the DSI add one and then update the E-ink with the new days then repeat.
To reset the DSI I plan on having a button to wake it from deep sleep and reset it and get the current time from NTP to make it sleep until the next day then go back to sleep until that time and repeat.

Also I need to be able to connect to the esp32 to set up the wifi, but I don't know how to do that efficiently. My current plan is to have it host a webserver on it when you press the resent button for 60 seconds, but if there is a way to detect if someone connected to the webserver and not turn off until they leave it that would probably be better.

If there is a better way to do this, please let me know and if there are better/cheaper ways to power an esp32 for a long time I would love to know, ideally it should last from 6-12 months as I estimate that the current method should last in that range. Also this is on a budget to be as cheap as possible, around $60-70 (Larger e-inks are pricey).

Use 2xAA Battery, that's way enough.

I should have mentioned I want it to be rechargeable over usb c. Sorry!

To recharge it every 5 years?

Huh, well that changes things. How would I use them, could I just hook them up to the VIN or do they have to go through something else. Also, how would I ensure that it is a constant voltage since AAs have a very steep voltage drop-off.

Full 2xAA is ~ 3.2V, but the ESP32 would like 3.3V --> use a stepup/stepdown e.g. Pololu 3.3V Step-Up Step-Down Spannungsregler S7V8F3 - Eckstein Shop, 9,95 € - you'll find a lot around.

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