Upgraded to latest build (VyOS 1.4-rolling-202103251004). Route is now correctly displayed inside VRF (syntax still does not match doc btw).
But VRF routing still showing unreachable default route :
vyos@vyos:~$ sh ip route vrf mgmt
Codes: K - kernel route, C - connected, S - static, R - RIP,
O - OSPF, I - IS-IS, B - BGP, E - EIGRP, N - NHRP,
T - Table, v - VNC, V - VNC-Direct, A - Babel, D - SHARP,
F - PBR, f - OpenFabric,
> - selected route, * - FIB route, q - queued, r - rejected, b - backup
VRF mgmt:
K>* 0.0.0.0/0 [255/8192] unreachable (ICMP unreachable), 00:05:29
S>* 10.10.5.0/24 [1/0] via 10.20.252.254, eth0, weight 1, 00:00:18
C>* 10.20.252.0/24 is directly connected, eth0, 00:00:18
I have the feeling that this default route is inherited from outside VRF.