The comments to my question suggest to disable the first DHCP server which is proably a valid thing to do. However, I do not seem to have any troubles so far running two servers, because the second one is non-authorative and the ranges are separated. He seems to hand out two IPs so far to my two test clients. (I might edit my answer if I recognise issues.)
Also: Switching my ISP router's local DHCPv4 server to off just seems to turn it non-authorative since I still can edit static IPs for MAC addresses in the GUI after switching off. So local seems to stand for "the locally responsible".
Even in the case I could disable the first DHCP server I still would face this:
My clients did not receive a route to the tunnel from my own DHCP server. This can be accomplished by configuring the DHCP server to hand out static routes.
Caution: It will then not hand out the default gateway any more, unless you define it as another static route: https://ral-arturo.org/2018/09/12/dhcp-static-route.html
So the solution to my problem is not to setup a second (default) gateway, but to configure DHCP so it will hand out the routes that my clients need.
My /etc/dhcp/dhcpd.conf looks like this:
#authoritative;
default-lease-time 86400;
max-lease-time 86400;
option rfc3442-classless-static-routes code 121 = array of integer 8;
option ms-classless-static-routes code 249 = array of integer 8;
subnet 192.168.111.0 netmask 255.255.255.0 {
range 192.168.111.223 192.168.111.254;
option routers 192.168.111.1;
#deny unkown-clients;
option domain-name-servers 192.168.111.1;
option domain-name "local";
option rfc3442-classless-static-routes 24, 192, 168, 1, 192, 168, 111, 222;
option ms-classless-static-routes 24, 192, 168, 1, 192, 168, 111, 222;
}
host squeezeboxtest {
hardware ethernet 00:04:20:5f:55:8e;
fixed-address 192.168.111.231;
option host-name "squeezeboxtest";
}
host asusklein {
hardware ethernet 04:e6:76:5d:cf:a6;
fixed-address 192.168.111.232;
option host-name "asusklein";
}
host HAPZE {
hardware ethernet fc:f1:52:fc:a6:60;
fixed-address 192.168.111.21;
option host-name "Sony HAP-ZE";
}
The server can be restarted with
sudo systemctl restart isc-dhcp-server
Just as a note: It is possible to restrict clients from getting an IP from the second DHCP server by adding the line deny unkown-clients;.