Wired connection on Ubuntu became unavailabile after a RealTek ethernet driver update

How it started

Since I've installed Ubuntu 20.4 as a dual boot on my machine, I've had connectivity issues . Drivers were working out of the box but what was strange was that every couple of hours I would loose connection and not be able to connect again, until I restart.

But recently it has been happening like every hour, and since I'm working on my computer it's very annoying to restart it every hour or so. I thought it was my wireless card so I connected to wired connection to try to solve the issue, but the problem persists.

I tried installing a proper driver(https://www.realtek.com/en/component/zoo/category/network-interface-controllers-10-100-1000m-gigabit-ethernet-pci-express-software) for my Ethernet controller

$ lspci -knn | grep Eth -A3
03:00.0 Ethernet controller [0200]: Realtek Semiconductor Co., Ltd. RTL8125 2.5GbE Controller [10ec:8125] (rev 05)
    Subsystem: Gigabyte Technology Co., Ltd RTL8125 2.5GbE Controller [1458:75ca]
    Kernel modules: r8125
04:00.0 Network controller [0280]: Intel Corporation Wi-Fi 6 AX200 [8086:2723] (rev 1a)

But while following the instructions, I got this error:

How it's now

$ sudo ./autorun.sh 

Check old driver and unload it.
Build the module and install
Skipping BTF generation for /home/balsa/Downloads/r8125-9.006.04/src/r8125.ko due to unavailability of vmlinux
At main.c:160:
- SSL error:02001002:system library:fopen:No such file or directory: ../crypto/bio/bss_file.c:69
- SSL error:2006D080:BIO routines:BIO_new_file:no such file: ../crypto/bio/bss_file.c:76
sign-file: certs/signing_key.pem: No such file or directory
Warning: modules_install: missing 'System.map' file. Skipping depmod.
DEPMOD 5.11.0-40-generic
load module r8125
modprobe: ERROR: could not insert 'r8125': Operation not permitted
Updating initramfs. Please wait.
update-initramfs: Generating /boot/initrd.img-5.11.0-40-generic
Completed.

For far I've tried installing a driver from the repo (No ethernet connection available in Ubuntu 20.04)

$ sudo apt install r8168-dkms
Reading package lists... Done
Building dependency tree       
Reading state information... Done
r8168-dkms is already the newest version (8.048.00-1ubuntu0.20.04.2).
0 upgraded, 0 newly installed, 0 to remove and 23 not upgraded.

And it seems that driver is installed, although my controlled is labeled UNCLAIMED

$ sudo lshw -C network
[sudo] password for balsa: 
  *-network UNCLAIMED       
       description: Ethernet controller
       product: RTL8125 2.5GbE Controller
       vendor: Realtek Semiconductor Co., Ltd.
       physical id: 0
       bus info: pci@0000:03:00.0
       version: 05
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress msix vpd cap_list
       configuration: latency=0
       resources: ioport:3000(size=256) memory:a4400000-a440ffff memory:a4410000-a4413fff
  *-network
       description: Wireless interface
       product: Wi-Fi 6 AX200
       vendor: Intel Corporation
       physical id: 0
       bus info: pci@0000:04:00.0
       logical name: wlp4s0
       version: 1a
       serial: 64:bc:58:9e:77:a3
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical wireless
       configuration: broadcast=yes driver=iwlwifi driverversion=5.11.0-40-generic firmware=59.601f3a66.0 cc-a0-59.ucode ip=192.168.0.16 latency=0 link=yes multicast=yes wireless=IEEE 802.11
       resources: irq:19 memory:a4300000-a4303fff

Any help would be greatly appreciated !