"I thought that internet address were 2000::/3 and the rest were link local and private"
No. There specific prefixes allocated for link-local and ULA addresses. There are also other prefixes allocated for specific use (i.e. multicast, documentation, etc.). And there is the Global Unicast Address allocations.
All other prefixes are NOT ASSIGNED (yet) and MUST NOT be used - let's not repeat the mistakes done with IPv4 when someone started to use IPs they should never have used.
"Even a /56 is barely usable,"
It's up to 256 subnets - I would not call it "barely usable"
Biting the hand that feeds IT
