The network-online.target does not indicate “Internet access”. It mans there is a network interface available with an IP(not localhost) address added to it and there are routes for this IP address.
This does not mean Internet access, just that there is Networking available for the Network the system is directly connected to. If the system is directly connected to the internet, like a server, it means internet access, but this depends on the network the system is directly connected to.
The purpose of this target is to delay the start of services that needs a working network. It is not to monitor and “unreach” the target if the network is lost. After the boot is completed and all enabled services have started, the target is meaningless.
A little bit to read
https://www.freedesktop.org/wiki/Software/systemd/NetworkTarget/#conceptsinsystemd