If the AnyConnect client has been deleted by moving it to the recycle bin, the following procedure must be carried out for complete uninstallation (or before reinstallation is possible):

Enter "terminal" in the Spotlight search and open a terminal window. Then execute the following commands:

cd /opt/cisco
sudo find . | grep -i uninstall

Depending on whether in the output

./anyconnect/bin/anyconnect_uninstall.sh

or

./secureclient/bin/cisco_secure_client_uninstall.sh

is present, first execute the following command:

sudo ./anyconnect/bin/anyconnect_uninstall.sh

or

sudo ./secureclient/bin/cisco_secure_client_uninstall.sh

Then again

sudo find . | grep -i uninstall

If there are still uninstallers left, for each line

sudo <output line>

If the /opt/cisco directory has also already been deleted, then it gets a bit more elaborate.

pkgutil --pkgs | grep anyconnect

and

pkgutil --pkgs | grep secureclient

execute.

Then for each line:

sudo pkgutil --forget <package-name>.

For the base module, it should then look like this:

sudo pkgutil --forget com.cisco.pkg.anyconnect.vpn

Then install all the packages again (i.e. check all the boxes, contrary to the instructions) and uninstall them with the uninstaller so that no rubbish is left behind.
The --forget does not delete the actual programme package, but only makes the Mac forget that it was installed.