More research…
I have looked at the schematic for the XAIO Groove Shield that has battery management. If I read it and the XAIO schematic correctly, when USB power is present, +5 from the XAIO is an input to the battery management IC (U5) on the shield. The Vsys output of U5 is connected to the battery for charging. It is also connected to the input to the LDO 3V3 regulator on the shield. The 3.3v output of regulator would power everything on the shield. The output of that regulator is also connected to the 3V3 pin on the XIAO. That is how the XIAO receives its power.
When there is no USB connection present, there is no +5 input to U5 so U5 passes the battery voltage to the LDO regulator. That powers the shield and also powers the XAIO through the 3V3 pin.
My only problem with this approach is that in both cases, power is being applied to the output of another regulator. When USB power is present, the XAIO LDO regulator is producing 3.3 volts but since U5 is active and the battery is present, the shield LDO is also producing 3.3 volts. Both these regulators are on and producing 3.3 volts and are connected to each other. Is this OK?
When USB power is not present, there is no voltage to the input to the XIAO regulator so it is off. The battery voltage is at the input of the shield regulator and so it is on and producing 3.3 volts. That 3.3 volts is applied back to the XAIO and therefore also being applied to the output of the off XIAO regulator. Is this OK?
I may be completely missing something so please tell me where I am wrong. If I am right, please let me know that it is OK for the output of these two regulators to be connected to each other. If that is OK, I will do something similar for my project.
Thanks.