It is not the host-component of IPv6 that determines routability, it is the prefix.
If you have a link-local prefix (fe80::/10) then it is not global, if it is a private prefix (fc00::/7) then it also may not be global; if it is part of IANA's unicast allocation (2000::/3) it is global (firewall permitting).
There's an education here that unfortunately I don't have the time to give you.
SLAAC is the replacement for DHCP, it provides a local prefix address (fe80::) and optionally (and, crucially: additionally) provides a publicly routable IP if there's a public prefix available.
You can think of the subject being split into two components: