It drains battery because of VPN service solution, which is only non-rooted solution. Also if you use VPN (like Wireguard), you cannot use both.
Every app has own settings for allowing WiFi, data, VPN, background data connections natively in Android. I use custom ROM that has turned off internet connection for all apps by default and you need manually allow them to connect. Which solve mine problem with constant unwanted connections.
If you want really control over traffic on Android and combine with VPN, try ReThing DNS.