quick note for those spending weekends on labbing - if you want to log info (from Syslog for example), and the management interface is in separate VRF (very good idea), you need to configure VRF in two, or even three (if you count VRF definition itself) different places. if you forget one, it won’t work.

so, first of all, create management VRF definition:

!
vrf definition MGMNT
 rd 444:444 ! optional, but just to keep the numbering across VRFs
 !
 address-family ipv4
 exit-address-family
 !
 address-family ipv6
 exit-address-family
!

..then properly assign management interface to VRF:

!
interface GigabitEthernet0
 vrf forwarding MGMNT
 ip address 192.168.4.1 255.255.255.0
 ipv6 address 2001:db8:4::1/64
 load-interval 30
 negotiation auto
!

and finally, the logging via syslog - VRF is to be configured on both source-interface as well as host definition:

logging trap debugging
logging origin-id hostname
logging source-interface GigabitEthernet0 vrf MGMNT
logging host 192.168.44.254 vrf MGMNT

host with address 192.168.44.254 should start receiving logs - with the first one being most likely STARTSTOP:

Oct  9 06:34:11 192.168.44.1 edgerouter: 014464: Oct  9 2022 06:34:11 CEST: %SYS-6-LOGGINGHOST_STARTSTOP: Logging to host 192.168.44.254 port 0 CLI Request Triggered

good luck in VRFing. I mean, logging. in VRFs.