battery and smartwatch

hello everyone, I'm trying at the moment to make the smallest smartwatch possible. it will have a battery, an atmega238p-au, a hc-05, a ds1307 and a small oled screen. but I have a small problem: my battery provided 3.7v and 400mah. that's enough to power the atmega, but not enough for the ds1307 that runs in 5v. It should also be known that the voltage of the battery will decrease with the temp (it will go down to 3v) 3v is not enough to feed the hc-05, nor the oled screen.
so I found two shema that I put with my post (a charger and a booster) they are shema coherent that I found and that I would like to realize later on my pcb (first the charger and then the booster) and I would just like to know what you thought about it.
thank you :wink:

booster.png

I would especially like to know if the circuit will function