In all three logs "wlan0" is probed and appears to be present, and in the USB logs I also see wlan1 (and confusingly, wlan2) and those are then associating successfully to the network. I don't see any attempts from the wlan0 interface (the Broadcom card) to associate to a network.
Note that ConnMan stores SSID/pass data against a specific card, so even if you have connected successfully on wlan1/2 and then remove the USB card, it will not auto-connect to the network using wlan0. You would need to specifically connect without the USB device connected and (re)enter the passphrase. I'm wondering if you've done that?
That said, I'm also just realising that wlan0 is using the 'wl' driver:
Aug 06 08:25:54 LibreELEC kernel: wl: loading out-of-tree module taints kernel.
This driver is vendor/out-of-tree and has been unmaintained by Broadcom for more than a decade. It has been dropped from LE13 as it no longer compiles and I wouldn't be even slightly surprised if (even when it did compile) it didn't work properly on modern kernels due to long-term bit-rot. Some wl using cards are also supported by 'b43' which although in-kernel, is equally unmaintained for about a decade, and for that reason we haven't enabled it in LE13 kernels after dropping wl. TL/DR; even if this did work on LE12 it will have a short lifespan.
For that reason I'd recommend you get an alternative PCIe card. Look for something with an Intel chip as those are generally well maintained and with the drivers/firmware upstream.