LiPo battery powering low power MCU
Absolute maximum ratings are stress ratings after which you get permanent damage.

Operating of the device is not guaranteed above the normal operating range, and the long-term reliability may suffer. The datasheet conditions apply for being within the normal operating range.

It means, the device does not have to work properly above normal operating range.

The 3.7V is only nominal voltage for the LiPo cell. It can have more than 4.0V when fully charged. Even if you don't charge it in-circuit. Do not connect to battery directly. Diode is not the best either - depending on diode, with extremely light load, it won't drop much voltage.