There is an issue with VPN integration in WSL running on my Windows 10. You need to redirect WSL to VPN, please follow these steps:

STEP-1: Obtain DNS address from Windows Power Shell

>nslookup
Servidor predeterminado:  yyyy.com
Address:  x.x.x.x

or

>ipconfig /all

STEP-2 Open Ubuntu-20.04 Version 2 WSL and open /etc/resolv.conf

STEP-3 Modify /etc/resolv.conf . Add the VPN Address in the first position(I deleted the others directions but it is not necessary), save the file, and try to access again. My file looks like:

nameserver X.X.X.X

This worked for me.

How Anyconnect v4.9 breaks it: It adds a route for wsl2 with a low metric 2, lower than 5256, which causes vpn becomes the chosen route, and of course that will never work. As seen below. c:> route.exe print Note: “172.17.228.192 255.255.255.240” is the wsl2 destination subnet. 172.17.228.192 255.255.255.240 On-link 172.17.228.193 5256 172.17.228.192 255.255.255.240 10.255.0.1 10.255.0.71 2 This problem is solved when I change the vpn route metric to 5500, higher than 5256, by doing so: Control Panel – network – click the vpn – property – IPv4 – property, advanced – automatic metric: uncheck it and type in 5500.

source: https://riowingwp.wordpress.com/2020/12/13/anyconnect-bug/

WSL2 - VPN Fix:

There is an issue with DNS Forwarding in WSL2 when using VPN (see github Issue). Plus there is a issue with the Cisco AnyConnect. So here is a workaround for these problems. Should work for Ubuntu and Debian.

Workaround

1. Find out nameserver with windows powershell (during VPN Session)

   nslookup
   

   You'll get the IPv4 adress of your corporate nameserver Copy this address.

2. Disable resolv.conf generation in wsl:

   sudo nano /etc/wsl.conf
   

   copy this text to the file (to disable resolve.conf generation, when wsl starts up)

   [network]                                                                        
   generateResolvConf = false
   

3. In wsl Add your corporate nameserver to resolv.conf

   sudo nano /etc/resolv.conf
   

   Remove other entries and add your corporate nameserver IP (if you have a secondary nameserver, add it in a separate line)

   • nameserver X.X.X.X (where X.X.X.X is your address obtained in step 1)

4. Set your VPN adapter (if you have Cisco AnyConnect) open a admin powershell

   • Find out your VPN adapter name: Get-NetIPInterface (in my case: "Cisco AnyConnect")
   • Set adapter metric (Replace -Match with your name), in my case I have to run this after ever reboot or VPN reconnect:

   Get-NetAdapter | Where-Object {$_.InterfaceDescription -Match "Cisco AnyConnect"} | Set-NetIPInterface -InterfaceMetric 6000
   

   (What is interface metric: Used to determine route, windows use interface with lowest metric)

5. Restart wsl in powershell: wsl.exe --shutdown

6. Test it in wsl run: wget google.com - if this command works, you are done.

In my case I get DNS issues when try to connect to internal stuff via browser (on Windows 10, f.e.: intranet), caused by the high metric value set in step 4 (basically kind of disabling VPN Route). So here is the workaround for the workaround:

1. Check your default metric (of VPNs Interface) in powershell (replace -Match with your interface name)

Get-NetAdapter | Where-Object {$_.InterfaceDescription -Match "Cisco AnyConnect"} | Get-NetIPInterface

2. When running into problems on Windows 10 restore this default value with admin powershell (replace value at the end with your default value):

Get-NetAdapter | Where-Object {$_.InterfaceDescription -Match "Cisco AnyConnect"} | Set-NetIPInterface -InterfaceMetric 1

All that i needed from @kraego answer is

Get-NetAdapter | Where-Object {$_.InterfaceDescription -Match "Cisco AnyConnect"} | Get-NetIPInterface

I couldn't ping 8.8.8.8, but with the metric change it started to work.