The A2179 is an Intel MacBook Air with the T2 chip, so the Intel recovery key combinations apply.
Since you’ve already tried multiple networks, Ethernet, USB booting, and DFU revive/restore, I wouldn’t keep chasing the -2005F/-2100F errors as just a Wi-Fi problem. Apple says those Internet Recovery errors are generally network-related, but your troubleshooting has already ruled out most of the obvious network causes. How to start up from macOS Recovery - Apple Support
One thing I’d still try is each recovery method separately from a full shutdown:
- Command-R for the built-in Recovery system
- Option-Command-R for Internet Recovery and the latest compatible macOS
- Shift-Option-Command-R for the original/closest available macOS
If Command-R also won’t load, and a properly performed T2 DFU restore completes but the Mac still can’t enter Recovery or boot, I’d start suspecting a hardware problem rather than the replacement battery or macOS installation.
Apple’s DFU procedure is here: How to revive or restore Mac firmware - Apple Support
At that point, I’d have Apple or an AASP run hardware diagnostics before putting more parts into it.
