Let me try to describe my schema:
There is 12V acid battery constantly charged with DC 13.8v 500ma, on that power (battery) is connected attiny85 thru 78l33 voltage regulator + capacitor 470uf,
thru 7805 is powered ESP32 (it have own voltage regulator to 3.3v) with capacitor with same value. Devices communicate over I2C with 10K pullup resistors to 3.3V on attiny side. Wires are few inches long.
Everything works fine when there is external(charging) voltage, when I disconnect it, I2C bus stop working. I haven't trying to lower pullups or connect them on other side - ESP32 . I do not see the reason why that stop working when was powered on battery. (guess my knowledge is not enough :) )