Kernel drivers need to be compiled for the specific kernel version running and 'dkms' drivers automatically rebuild (recompile) when a change in the kernel version (magic) is detected. Compiling requires header files, so that's easily explained.
Logs show the hardware being probed and the wl driver loading. If that doesn't result in a working interface it's probably due to a difference between current kernel APIs and ageing/un-current driver code. The kernel evolves and moves (drifts) forwards while the driver code is static, so at some point the kernel has drfted far enough for things to stop working.
I have a suspicion the driver stopped working (although still compiled) some time ago, but few people use hardware old enough to need 'wl' these days (most people use Ethernet) so the breakage has gone un-reported.
As per earlier comments: a decent USB wifi stick or replacing the PCIe module are probably the best options. The latter is probably cheapest although cracking older 'mini' boxes open is quite a task.