Wireguard client can not connect to internet

I have installed Wireguard with following commands:

sudo apt update
sudo apt install wireguard

Then I have installed resolvconf:

sudo apt install resolvconf

Created keys:

umask 077
wg genkey | sudo tee /etc/wireguard/private.key
sudo cat /etc/wireguard/private.key | wg pubkey | sudo tee /etc/wireguard/public.key

Finally, created config:

sudo nano /etc/wireguard/wg0.conf
# below is the content of the config file
         [Interface]
         PrivateKey = omitted
         Address = 10.9.0.7/32
         DNS = 1.0.0.1

         [Peer]
         PublicKey = omitted
         AllowedIPs = 0.0.0.0/0, ::/0
         Endpoint = 95.87.101.10:51820

After executing sudo wg-quick up wg0 all my applications are left without internet. Internet comes back after I sudo wg-quick down wg0 Wireguard.

I do not have access to the server, it is maintained by the company.
I can only tamper with my own machine.

I am not skilled with networking, my company said to just follow above instructions and everything will work, but here is what I have tried to solve the problem:

I have tried suggestions from this question but no success.

sudo wg gave the following output:

interface: wg0
  public key: y5ZpnepnWHWBOvm04iDUh/+XgLIZKSOClI4It5D/ESU=
  private key: (hidden)
  listening port: 43460
  fwmark: 0xca6c
peer: KIkiNWfiSEGYbXAGvNau8kOlG8rqFfEFeNzPjnUzz0Q=
  endpoint: 95.87.101.10:51820
  allowed ips: 0.0.0.0/0, ::/0
  transfer: 0 B received, 296 B sent

I have assumed that handshake works, but something else obstructs internet connection.

ip route show gave me this:

default via 192.168.1.1 dev wlx3c7c3f49907c proto dhcp metric 600 
169.254.0.0/16 dev wlx3c7c3f49907c scope link metric 1000 
192.168.1.0/24 dev wlx3c7c3f49907c proto kernel scope link src 192.168.1.7 metric 600

After googling, I came to the conclusion that DHCP screws default route, but I do not know how to fix it. I have tried sudo ip route add default via 192.168.1.1 but that did not help either. ip route while Wireguard is on gives following output:

default via 192.168.1.1 dev wlx3c7c3f49907c 
default via 192.168.1.1 dev wlx3c7c3f49907c proto dhcp metric 600 
169.254.0.0/16 dev wlx3c7c3f49907c scope link metric 1000 
192.168.1.0/24 dev wlx3c7c3f49907c proto kernel scope link src 192.168.1.6 metric 600

I have tried sudo cat /proc/sys/net/ipv4/ip_forward but that did not help either.

This is the best I can do, since I do not know much about networking. I came across this site after googling so I have decided to ask for help, in a desperate hope that a solution will be found.

If you need further info leave a comment and I will reply.

... maybe you could try here

sudo nano /etc/wireguard/wg0.conf
below is the content of the config file
     [Interface]
     PrivateKey = omitted
     Address = 10.9.0.7/32
     DNS = 1.0.0.1

for DNS your own internet gateway or local dns/dhcp server (i.e 192.168.110.1) instead of DNS = 1.0.0.1 or another public DNS server.