2015 MacBook Air (13" - 256 SSD, 8GB RAM) Boot problems
If your installer/boot media works fine on a different Mac but fails on your MacBook Air, the issue is likely hardware (logic board).
You don't need a drive to load the installer.  If you boot from USB or boot from the network (Internet), it is caching the installer in memory.  If you're to run diskutil list command while the installer is running, you'll find many &quot;disks&quot; from 0 to 20-something.  These are the RAM disks and this is normal.
What you've done by booting both Internet Recovery and USB installer is bypass a potential failure point - the internal storage device.  The fact that the problem still exists  using both of those methods indicates you have logic board issue (possibly CPU or memory).  By booting from Internet, you remove both the USB bus and the internal storage from the equation.  Process of elimination says there's nothing more to bypass - the problem is with your main board.
Apple (service) isn't going to do anything that you've already done.  Apple won't repair this - they will quote you for a logic board replacement.  This normally runs about $5-700 USD.  At that price point, I'd go for a new machine.
Also Sell that one as salvage and recoup some money.  The screen is good, the battery, case, keyboard, trackpad, etc. can all be used for repair parts by a shop.  Even the logic board can be salvaged for individual components (the SMC chip is in high demand).