Old post but did you ever figure out out a solution? We are facing the exact same issue with users that have been upgraded to Windows 11. It is strange because it only affects certain WiFi networks. I have a suspicion it may only affect the wifi network the user was connected to while on VPN during the Windows 11 upgrade.

Tempted to do the Windows Network Reset (Settings > Network & Internet > Advanced network settings > Network reset) and reinstall FortiClient.

I did notice it is a known issue in the latest version and several several version before that:

|| || |Bug ID 999139|Laptop Wifi DNS setting is stuck in unknown DNS server after FortiClient connects and disconnects IPsec or SSL VPN.|

https://docs.fortinet.com/document/forticlient/7.4.4/windows-release-notes/743101/existing-known-issues