For future reference (and in case anybody else needs to know).
My Fossil watch (Grant Collection, FS 4736) takes a SR621SW type battery.
Naturally, it’s a different type of battery than all the other button cell using devices I have.
Also for future reference, this is a nice cross-reference chart for button cell/watch batteries.
Just leaving a note to myself for future reference.
Needed to rebuild the kmod-wl package because of a borked update process (something made the computer crash mid-update).
A bit of Google searching brought me to the script in
sudo /usr/sbin/akmods --from-kernel-posttrans --kernels `uname -r` rebuilt the missing kmods and a
modprobe wl got the wifi back up and running.
sudo /usr/sbin/akmods --force (for the current kernel) or
sudo /usr/bin/akmods --force --kernels kernel version (for a specific kernel) works as well.