Cannot connect to the wired internet on Ubuntu 20.04

I have an issue similar to what is described here. I tried all the answers in that posting as well as other similar questions with no luck. I have also zero understanding in networking and really need help with it. The fresh installation worked fine,but then I have probably run the system upgrade and since then the internet access is broken. One thing I have noticed that when modifying nameserver line in /etc/resolv.conf ,the NetworkManager always resets it to 127.0.0.53. I tried disabling that service, deleting the resolv.conf but it always returns.I will update the question with any extra info on request.

I have tried also this solution. But when pinging google.com I am getting:

ping: google.com:Temporary failure in name resolution

Here is the relevant output from lspci:

03:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd.
        RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 15)

And lshw -c network:

*-network                 
    description: Ethernet interface
    product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller
    vendor: Realtek Semiconductor Co., Ltd.
    physical id: 0
    bus info: pci@0000:03:00.0
    logical name: enp3s0
    version: 15
    serial: 4c:cc:6a:2b:b7:05
    size: 100Mbit/s
    capacity: 1Gbit/s
    width: 64 bits
    clock: 33MHz
    capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt-fd autonegotiation
    configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=5.11.0-43-generic duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.0.105 latency=0 link=yes multicast=yes port=twisted pair speed=100Mbit/s
    resources: irq:19 ioport:d000(size=256) memory:df104000-df104fff memory:df100000-df103fff

I have also tried to boot in secure mode and from the installation USB and same problem persists. It can't be a hardware issue as I have Windows in dual boot there which connects to the internet fine. I updated the above: when loading from installation Flash disk the wired internet does work.

Here is the output of sudo service systemd-resolved:

systemd-resolved.service - Network Name Resolution
    Loaded: loaded (/lib/systemd/system/systemd-resolved.service; disabled; ve>
    Active: inactive (dead)
    Docs: man:systemd-resolved.service(8)
    ...

After I have restarted the service I am getting this:

systemd-resolved.service - Network Name Resolution
    Loaded: loaded (/lib/systemd/system/systemd-resolved.service; enabled; vendor preset: enabled)
    Active: active (running) since Fri 2022-01-21 16:03:30 EET; 9s ago
    Docs: man:systemd-resolved.service(8)
                 https://www.freedesktop.org/wiki/Software/systemd/resolved
                 https://www.freedesktop.org/wiki/Software/systemd/writing-network-configuration-managers
                 https://www.freedesktop.org/wiki/Software/systemd/writing-resolver-clients
    Main PID: 2826 (systemd-resolve)
    Status: "Processing requests..."
    Tasks: 1 (limit: 19082)
    Memory: 4.7M
    CGroup: /system.slice/systemd-resolved.service
    └─2826 /lib/systemd/systemd-resolved

Starting Network Name Resolution...
Positive Trust Anchors: 
    systemd-resolved[2826]: . IN DS 20326 8 2
    e06d44b80b8f1d39a95c0b0d7c65d08458e880409bbc683457104237c7f8ec8d  
    systemd-resolved[2826]: Negative trust anchors: 10.in-addr.arpa
    16.172.in-addr.arpa 17.172.in-addr.arpa 18>   systemd-resolved[2826]: Using system hostname 'sasmaster-ubuntu20'.   systemd[1]:

Started Network Name Resolution.