Local name resolution fails intermittently when connected to VPN

[Mauro]

When I connect to my company Cisco ASA using the official Any Connect VPN client, my system receives a new DNS server which is on the local network I'm connecting to with the VPN, which is 192.168.240.250. Once the VPN connection is established, all DNS queries are directed to this server and hence I can resolve both public names (like google.com) and local names (like myserver.companydomain names, which resolve to 192.168.240.x IP addresses).

When I use the Network Manager openconnect plugin to connect to the same VPN, this works the same, but intermittently I get DNS resolution errors for local names, just like if the query were directed to the wrong server (perhaps the ISP DNS server?) or if some kind of caching provided by systemd-resolved were returning stale failed results.

At first I thought I was hitting:
https://bugs.launchpad.net/ubuntu/+source/network-manager-openconnect/+bug/1096326
however, I learnt that Ubuntu 20.04 is not using dnsmasq, so the problem must not be the same.

Then I found:
https://bugs.launchpad.net/network-manager/+bug/1624317
which however is marked as fixed in Zesty and Artful. Some people there suggest to change the default priority of the DNS server for the VPN connection, but this does not fix the problem for me.
In comment #110 (https://bugs.launchpad.net/network-manager/+bug/1624317/comments/110) someone suggested it was not still working in Artful and that the only solution is to completely disable systemd-resolved, but I honestly don't know which are the consequences of such a choice. No one replied to him any more.

So far, the only workaround I could find, whenever DNS queries start failing, is to issue a systemd-resolved restart:
sudo systemctl restart systemd-resolved.service

After I do this, resolution of local names start to work again.
Some days I have to do this a couple of times in the whole day, some others I have to issue it multiple times within few minutes...

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: network-manager-openconnect 1.2.6-1
ProcVersionSignature: Ubuntu 5.4.0-53.59-generic 5.4.65
Uname: Linux 5.4.0-53-generic x86_64
ApportVersion: 2.20.11-0ubuntu27.12
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: KDE
Date: Mon Nov 23 16:06:42 2020
InstallationDate: Installed on 2020-10-05 (48 days ago)
InstallationMedia: Kubuntu 20.04.1 LTS "Focal Fossa" - Release amd64 (20200731)
SourcePackage: network-manager-openconnect
UpgradeStatus: No upgrade log present (probably fresh install)