The SAN configuration specifies how to allocate the raw storage space to different user volumes and error correction.
The SAN itself doesn't need a complex operating system, as all it does is shovel data from one side to the other. There is still a minimal system that gives configuration access, but you wouldn't interact with that during normal use.
The servers that use the SAN only have instructions to contact the SAN and provide specific credentials, the SAN then replies with a list of volumes configured for those credentials, including their sizes.
So space isn't "taken" by servers, but rather "given" to them.
The actual communication between the server and the SAN can work in different ways -- the cheapest variant is to use Ethernet and the iSCSI protocol, but there are also dedicated controller cards that have local caches, use a protocol that has lower latency and higher throughput than Ethernet, and provide a BIOS extension to allow booting directly from the SAN without requiring extra mainboard features.