Arduino Nano 33 battery power/charging
The VIN (and the USB) goes into a 3.3V switching regulator. This has a minimum input voltage of 4.5V.

You isolate the output of that regulator from the rest of the circuit by cutting that one link (which is easy to re-solder). You are then free to feed 3.3V from your own power source directly into the board. 

Yes, if you provide more than 3.3V you are liable to damage the board (note that a Li-Poly can be around 4.2V when fully charged). 

You need to take your battery power and feed it through a nice efficient switching voltage regulator that has a low enough "dropout" voltage to allow good use from the battery. Note that many devices "rated" at 3.3V will also work much lower. For example:


Nina-B3 series module will run at down to 1.7V. 
The APDS-9960 will operate down to 2.4V. 
The HTS221 will run at down to 1.7V.
MP34DT06J can go as low as 1.6V.
LSM9DS1 can run from 1.9V.
LPS22 is 1.7V minimum


So it could be good to reduce your power to 2.5V instead of 3.3V to give more life from the battery. You should check each of the components in the both the device schematic and the rest of your circuit (by reading the datasheets) to find the highest "minimum" voltage they will work on.