Custom DNS server is not working
Solution 1:
In your system settings screenshot, you currently have "Automatic" enabled next to the field where you enter your custom DNS IP address.
You should disable "Automatic" for DNS. Once you do that, DNS requests should be queried from the IP address you specify in the field.
Keep in mind that individual applications might not use the DNS server that you specify in your system settings. Examples include Tor, VPN clients, and potentially even your web browser. Notably, there has been a trend for apps to move to using DoH since it is more secure and more private than typical DNS lookups which are sent in plaintext.
Getting your DNS server to work for these applications will generally need to be configured for each application in their settings. For example, Firefox has been pushing DoH lately, but you can opt-out.