Missing WiFi icon on macOS Big Sur recovery mode

Wi-Fi is likely perfectly available, but you can't fiddle with its settings.

If you have a working version of MacOS on your drive, it is far, far easier to download and install from inside MacOS.

How to upgrade to macOS Big Sur - Apple Support

If you need to re-install Mac OS for some reason, this article describes the process in the (severely restricted) environment of Recovery mode:

How to reinstall macOS - Apple Support

.

Recovery Mode depends on having a simple, accessible Wi-Fi capability to function at all. If your Wi-Fi is too complicated, it cannot work.

Recovery provides DiskUtility and Installer services, along with a very few others.

Recovery does not allow you to change Wi-Fi parameters, and does not provide general-purpose Wi-Fi for your use. You will not see the Wi-Fi Icon on the Menubar.

Based on that picture, your Mac is working as designed.

Click on the Apple icon. Click on System Preferences. Click on Dock & Menu Bar. Click on Wi-Fi on the menu bar on the left side. Check the box to 'Show in Menu Bar'.

Let readers know if you get stuck on something. We all want you to be able to enjoy using your Mac.