Dns problem in manjaro gnome

Your issue is not a basic issue with Manjaro - but a local network configuration.

Such issue is is next to impossible to troubleshoot remotely.

The first step is to restart your router and thus the dns service.

Undo/Revert any customization you may have made in networkmanager.

/etc/resolv.conf is controlled by the resolvconf program and written by NetworkManager.

You can control resolvconf using the /etc/resolvconf.conf file to set a specific nameserver - and this is great for troubleshooting. It is highly recommended to locate the actual issue interfering with setting a nameserver

/etc/resolvconf.conf

name_servers 8.8.8.8

run resolvconf to update the resolv.conf

sudo resolvconf -u

then reset your network (from your inxi the eno1 is your nic)

sudo ip link set eno1 down
sudo ip link set eno1 up

systemd-resolved

In some situations it may help to remove openresolv package and enable systemd-resolved.service.

sudo pacman -R openresolv
sudo systemctl enable --now systemd-resolved.service