Comment 16 for bug 2022826

You should not need any DKMS packages nor an OEM kernel. The stock Ubuntu kernel supports your NIC natively. Remove the DKMS modules and reboot into the 5.19 kernel and post the dmesg output from that boot.

lsmod should list the r8169 module.

And:
$ modinfo r8169 | grep 8125
firmware: rtl_nic/rtl8125b-2.fw
firmware: rtl_nic/rtl8125a-3.fw
alias: pci:v000010ECd00008125sv*sd*bc*sc*i*

And the firmware should be there as well:
$ ls -la /lib/firmware/rtl_nic/rtl8125*
-rw-r--r-- 1 root root 3456 Apr 21 07:41 /lib/firmware/rtl_nic/rtl8125a-3.fw
-rw-r--r-- 1 root root 10128 Apr 21 07:41 /lib/firmware/rtl_nic/rtl8125b-1.fw
-rw-r--r-- 1 root root 3328 Apr 21 07:41 /lib/firmware/rtl_nic/rtl8125b-2.fw