I was finally able to solve this by setting up a DHCP server myself on the same network, which configures the correct Search Domain to send to the clients. Once I had a dhcp server, in my case isc-dhcpd with the configuration in dhcp.conf: option domain-name "myrealdomain.tld"; Android was able to resolve local A-records set in my DNS server.

Connect to a PPTP VPN from your Android phone - TechRepublic Jan 21, 2011 How to update the DNS settings on your iPhone | iMore Apr 02, 2018 How to push my own DNS server to OpenVPN? - Server Fault

The Domain Name System (DNS) is a central part of the Internet, providing a way to translate a domain name for a website you’re seeking into a numeric Internet Protocol (IP) address. Anything connected to the Internet – laptops, tablets, mobile phones, websites, etc. – relies on DNS to accurately associate domain names with their corresponding IP […]

A Smart DNS or Domain Name System is used to translate a website address into a specific IP address of the server that a user should connect to. It’s usually marketed by companies as a tool to unblock geo-restricted content by rerouting a user’s geolocation through a proxy server. How to Change DNS Servers on Android? | hide.me Mar 01, 2019 DNS over Sonicwall VPN - Spiceworks

DNS over Sonicwall VPN - Spiceworks

How To Change The DNS In Windows 10 - vpn.surf If you ever used Google to search for a website, then you have definitely used a DNS. The DNS or Domain Name System is the directory of the internet which translates the web addresses into their respective IP addresses.. This process happens within milliseconds but some DNS servers are faster than others.