lspci -nnk | gre -A3 Net shows a Network controller  Broadcom Inc. and subsidiaries BCM4311 802.11/g WLAN [14e4:4311] device. Both in live and installed, the driver being used is b43-pci-bridge.
The difference is that in live, the loaded kernel modules show only ssb. Installed shows ssb and wl.
mhwd -l shows the driver network-broadcom-wl version 2018.10.07 being used. The output has no changes compared to running it live.
I read the link you suggested and I see it recommends a classic driver for my device, but I have to admit that the blacklisting instructions are a bit confusing to me, considering I have no access to internet in said computer (I’m not sure how the preferred driver/module will be installed).
Drivers in linux are Modules. They are builtin or sometimes added and can be loaded. Linux can probing drivers and use a module automatically. You need to blacklist some modules that the probing expect to probe. Or remove a module and load the right one.
Lets say you have these modules:
manually you can remove a module from the list temporary:
and manually you can load a module from the list temporary:
b43 is the reveres-engineered module
To make it easier. If you don’t want, that the b43 module will be used, then blacklist it:
Create a file blacklist.conf in /etc/modprobe.d/ and write “blacklist b43” into the text file :