I created a /etc/NetworkManager/dispatcher.d/22showenv script, executable, with this content:

#!/bin/sh
exec > "/tmp/nm-$1-$2.log"
echo "Args: $*"
echo "Env:"
env | sort
exit 0

I have a system with a wired eth0 interface managed by NM, that uses DHCP to obtain information and lives on the 172.31.1.0/24 subnet with a gateway and DNS proxy server living on 172.31.1.1.

After adding the above script, I brought up my openconnect VPN connection via NM, and I saw that the above script created a file "/tmp/nm-tun0-vpn-up.log" which seemed OK, but the content was all wrong: it contained all the information about my eth0 connection, and nothing related to the new VPN tun0 connection.  A slightly edited listing of the output file is:

# cat /tmp/nm-tun0-vpn-up.log
Args: tun0 vpn-up
Env:
CONNECTION_UUID=<uuid>
DHCP4_BROADCAST_ADDRESS=172.31.1.255
DHCP4_DHCP_LEASE_TIME=86400
DHCP4_DHCP_MESSAGE_TYPE=5
DHCP4_DHCP_REBINDING_TIME=71811
DHCP4_DHCP_RENEWAL_TIME=39411
DHCP4_DHCP_SERVER_IDENTIFIER=172.31.1.1
DHCP4_DOMAIN_NAME=localnet
DHCP4_DOMAIN_NAME_SERVERS=172.31.1.1
DHCP4_EXPIRY=1294411827
DHCP4_HOST_NAME=hostname
DHCP4_IP_ADDRESS=172.31.1.105
DHCP4_NETWORK_NUMBER=172.31.1.0
DHCP4_ROUTERS=172.31.1.1
DHCP4_SUBNET_MASK=255.255.255.0
IP4_ADDRESS_0=172.31.1.105/24 172.31.1.1
IP4_DOMAINS=localnet
IP4_NAMESERVERS=172.31.1.1
IP4_NUM_ADDRESSES=1
IP4_NUM_ROUTES=0
PWD=/

However, the correct information is set in /etc/resolv.conf etc.  Not sure if this is really an openconnect bug; not sure who is responsible for setting this information and invoking the dispatcher scripts.