What was the original problem that has you trying to reinstall macOS? That same issue may be the same reason you are having issues reinstalling macOS.
I've never encountered a need for an Internet connection to reinstall macOS from a bootable macOS USB installer on the older non-USB-C Macs. I also have never tried to reinstall macOS while FindMy is turned on so I don't know if that could be a reason. Unfortunately this cannot be changed if you cannot access the Internet with this laptop.
FYI, the Thunderbolt port in the Airs can get really dirty so it may not be able to register any adapters or at least not be able to transfer data properly.
Try power cycling the router and possibly the modem making sure to wait at least five minutes for them to finish booting before attempting to access Recovery Mode or the online Apple Diagnostics.
Try an SMC Reset and PRAM Reset (hold the PRAM Reset for at least three chimes).
While I personally like to keep older hardware running as long as possible, I don't think it makes any sense to spend money on repairing such an old laptop even if it is a 2017 model (A1466 is a designation for a MBAir from 2012 to 2017). You can get the exact model by entering the system serial number on the check coverage page here, but please don't post the serial number on the forums since it is considered personal information:
Check Your Service and Support Coverage - Apple Support
