VPNv4 is the "transport". Your VRF route-targets match on both devices. Long story short, RT is extcommunity that is sent over VPNv4 session in BGP update. If one of local import RTs matches received extcommunity, routes are being imported in VRF with this RT configured. Actually VPNv4 is quite complex and complete explanation is beyond the scope of this site.
VPNv4 is not required in order to run routing protocol inside VRF. Cisco calls it VRF-lite. Your problem with
Active
state here is related to routing.address-family ipv4 neighbor 11.11.11.11 activate no auto-summary no synchronization exit-address-family ! address-family ipv4 vrf TEST22 redistribute static metric 10 neighbor 11.11.11.11 remote-as 1 neighbor 11.11.11.11 ebgp-multihop 2 neighbor 11.11.11.11 update-source Loopback0 neighbor 11.11.11.11 activate no synchronization exit-address-family
Both IPv4 and IPv4 vrf ATEST22 address families have Lo0 as the source. As long as IPv4 adjacency is Established
I assume Lo0 is not in VRF. That makes your BGP source inaccessible.