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I think you're not getting (m)any answers because there are not many off-the-shelf options for this, especially in a form suitable for a clamshell design.
If you require 5V output, depending on level of experience, you could try the ti.com website, on their 'Power Management' page they have an online tool called WEBENCH which will allow you to type your requirements and it will output a complete circuit diagram and bill-of-materials. TI also has some parts for LiPo charging, the datasheets will describe the circuits.
You'll need some experience in PCB design and closely have to follow the parts datasheets. If you want something off-the-shelf (i.e. ready-made PCB or module), I'm not aware of much, see the website here for some ideas: https://uk.pi-supply.com/products/pijuice-standard
There's also a possibility portable LiPo USB chargers for mobile phones could be investigated in case any support the requirements.
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You need to keep in mind that as you boost the voltage (from 3.7 to 5.0) you also increase the current drawn from the battery. The required current at a battery voltage of 3.7V is roughly 4.25A in order to deliver 5.0V at 3.0A ((5.0V/3.7V) * (3A/.95) where 0.95 is the assumed efficiency of the boost circuit). The current draw will vary with the battery voltage (inversely proportionally).
There are many boost converters that can perform in this range, so just shop around.
I'm designing a handheld Raspberry Pi 4 computer in a clamshell case with built in keyboard and game controls.
I'm using a touchscreen instead of a mouse, since the computer is not intended for video editing or graphical work.
The Pi website recommends a 2.5 amp supply for just the Pi, and the screen pulls 400ma.
My question is where do I get a reliable charge circuit / power supply that can output 3 amps? I'll be using the biggest flat 3.7v battery that will fit in the case.