Apple branded hardware is notoriously difficult to get working.
My personal opinion is - Apple do not want their branded hardware to run anything but macOS. As they also put in all kind of obstacles to avoid the other way around - macOS on non Apple hardware. There is so many stories everywhere about how difficult it is to decouple decommissioned Apple hardware from the OS. Yours is just one added to the list.
This article on the Arch wiki is most likely your best entry point
Some quotes to get you started
lspci -vnn -d 14e5
The compare your output with the list of supported the devices
As I understand the article - there is three kinds of driver
- The reverse engineered driver b43
- The mainline kernel driver brcm80211
- The restricted driver broadcom-wl
Dive into the Arch wiki and if that is not enough there is a huge amount of results when searching the web.
Before you apply the dkms related packages please be sure to read this topic - it will get you through the dkms without hickups.
More resources
- linux BCM4322 at DuckDuckGo
- [SOLVED] wireless interface doesn't find any access point / Installation / Arch Linux Forums
- MBP 7,1 Broadcom BCM4322 wifi not working - Drivers - Manjaro Linux Forum
- Search results for 'macbook broadcom' - Manjaro Linux Forum
- Manjaro and AUR - history - license - responsibility
- MacBookPro7,1 - ArchWiki
- AUR (en) - Packages