Typically, when you connect to a virtual private network (VPN), the operating system of your device closes all existing Internet connections and then re-establishes them through the VPN tunnel.
A member of the Proton community discovered that in iOS version 13.3.1, the operating system does not close existing connections. (The issue also persists in the latest version, 13.4.) Most connections are short-lived and will eventually be re-established through the VPN tunnel on their own. However, some are long-lasting and can remain open for minutes to hours outside the VPN tunnel.