Looking for information on 3000mAh LiPo Battery

Another thing to be wary about. Most TP4056 boards are set to 1Amp.
The above one is set to 780mA charge current.
Leo..

No it will not.

Your latest schematic will also not work since the MT3608 is not specified to work at 0% duty.

Yes there is:
About this item
• Charging Method: The recommended charging current is 0.6A, the maximum does not exceed 3A. The discharge current is recommended 1.5A, and the maximum does not exceed 3A
• Overcharge Protection: When charging the battery, when the voltage reaches the highest battery voltage (4.2V), the protection board will automatically power off and shut down, indicating that it will not continue to charge when fully charged, forms overcharge protection
• Over-discharge Protection: When the battery is about to run out and the voltage is as low as 3.0V, the protection board will also be turned off and can no longer be discharged, forming an over-discharge protection effect
• Short Circuit Protection: When an accidental short circuit occurs, the protection board will automatically shut down within a few milliseconds and will not be powered on again. Note that the cell is short-circuited (not through the protection board). The protection board will also fail due to continuous high current, or the components are heated and damaged
• Note: The battery overcurrent protection is not a panacea, do not continue to charge and discharge the current and voltage with a large current beyond the range, otherwise the protection board will be damaged and invalid

However it does not matter as you schematic will not work.

You need to switch between the USB Vbus and the MT3608 output.