From your dmesg output, I would guess that the proprietary broadcom-wl driver, available in the RPM Fusion repos, covers the 4360 chip:
$ dnf info broadcom-wl
Updating and loading repositories:
Repositories loaded.
Available packages
Name : broadcom-wl
Epoch : 0
Version : 6.30.223.271
Release : 24.fc41
Architecture : noarch
Download size : 24.0 KiB
Installed size : 38.4 KiB
Source : broadcom-wl-6.30.223.271-24.fc41.src.rpm
Repository : rpmfusion-nonfree
Summary : Common files for Broadcom 802.11 STA driver
URL : https://www.broadcom.com/support/download-search?pg=Legacy+Products&pf=Legac
: y+Wireless&pn=&pa=&po=&dk=&pl=
License : Redistributable, no modification permitted
Description : This package contains the license, README.txt and configuration
: files for the Broadcom 802.11 Linux STA Driver for WiFi, a Linux
: device driver for use with Broadcom's BCM4311-, BCM4312-, BCM4313-,
: BCM4321-, BCM4322-, BCM43142-, BCM43224-, BCM43225-, BCM43227-,
: BCM43228-, BCM4331-, BCM4360 and -BCM4352- based hardware.
Vendor : RPM Fusion
If you’d want to give it a go, I would suggest the following:
Uninstall the above mentioned layered packages, or rebase to the deployment previous to those installations. This is just to make sure there will be no conflicting packages, but can be skipped initially.
Install/layer the RPM Fusion repos if not already installed. Instructions here for Silverblue as well.
Reboot into the new deployment.
Install/layer the broadcom-wl package (rpm-ostree install broadcom-wl).
Remember that when the time will come to upgrade/rebase to a new major version (F42 in this case), there might be a need to temporarily remove the layered RPM Fusion repos. At least this was the way to go when upgrading Silverblue from F40 to F41 (see the FAQ section from this Fedora Magazine article).