Raspberry Pi UPS circuit review request + improvements
This situation depends on the functionality of the "OUT" pin of the charging module. The following is referencing your original schematic.  Your second schematic is invalid, as the charging circuit is expecting the storage cell to be isolated:

If the "OUT" is always active, then you don't need the MOSFET or the diode.  If it only switches on whenever the input power is no longer present, then you just eliminate the MOSFET(unless the "OUT" pin doesn't have some sort of PN junction on it's output already, which it likely does) or replace it with another diode.

In either case, the charging circuit you are currently using is only specified to output 1 Amp of current, which is WAY too little to power a RaspberryPi.