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Set wicd to use dhclient

Set wicd to use dhclient and duplicated static address

[My network]
afterscript = None
dhcphostname = hass
postdisconnectscript = None
dns_domain = hass
gateway = 192.168.0.1
use_global_dns = 0
lastused = True
ip = 192.168.0.113
beforescript = None
encryption_enabled = 0
broadcast = None
netmask = 255.255.0.0
usedhcphostname = 0
predisconnectscript = None
enctype = None
default = 0
dns2 = 8.8.8.8
search_domain = None
use_static_dns = 1
dns3 = None
profilename = My network
dns1 = 192.168.0.1

Seems wicd uses networking and its hooks are raised, wicd itself has no hook configured.

EDIT2:

I disabled dhcpcd.service and leave old (deprecated??) networking.service.

auto eth0
allow-hotplug eth0

#iface eth0 inet dhcp

iface eth0 inet static
    address 192.168.0.113
    netmask 255.255.0.0
    gatevay 192.168.0.1

Modified /etc/wpa_supplicant/ifupdown.sh not to touch wired interfaces

# quit if we're called for the wired interface
if [ "$IFACE" = eth0 ]; then
        exit 0
fi

Disabled avahi-daemon

Set wicd to use dhclient

It works now as real static address till I switch on WiFi in wicd. It removes eth0 IP address as support only swuitching among interfaces. Seems daemon /usr/share/wicd/daemon/monitor.py won't refresh cable. It just keep logging

2020/06/09 11:12:00 :: ifconfig eth0
2020/06/09 11:12:05 :: ifconfig eth0
2020/06/09 11:12:10 :: ifconfig eth0
2020/06/09 11:12:15 :: ifconfig eth0

When I killed daemon and run from command line I see reconnecting and IP refresh on eth0

sudo /usr/share/wicd/daemon/monitor.py
Starting automatic reconnect process
Starting automatic reconnect process
Starting automatic reconnect process
Starting automatic reconnect process
Starting automatic reconnect process

I this state it is not correct but at least seems Raspi can survive eth0 link changes (until I touch wicd in GUI).

avahi status

sudo systemctl status avahi-daemon.service 
● avahi-daemon.service - Avahi mDNS/DNS-SD Stack
   Loaded: loaded (/lib/systemd/system/avahi-daemon.service; enabled; vendor preset: enabled)
   Active: active (running) since Tue 2020-06-09 00:23:55 CEST; 8h ago
 Main PID: 280 (avahi-daemon)
   Status: "avahi-daemon 0.7 starting up."
    Tasks: 2 (limit: 2200)
   Memory: 1.1M
   CGroup: /system.slice/avahi-daemon.service
           ├─280 avahi-daemon: running [hass.local]
           └─361 avahi-daemon: chroot helper

čen 09 00:24:40 hass avahi-daemon[280]: Registering new address record for 192.168.0.113 on eth0.IPv4.
čen 09 00:24:54 hass avahi-daemon[280]: Withdrawing address record for 192.168.0.113 on eth0.
čen 09 00:24:54 hass avahi-daemon[280]: Leaving mDNS multicast group on interface eth0.IPv4 with address 192.168.0.113.
čen 09 00:24:54 hass avahi-daemon[280]: Interface eth0.IPv4 no longer relevant for mDNS.
čen 09 00:25:04 hass avahi-daemon[280]: Joining mDNS multicast group on interface eth0.IPv4 with address 192.168.0.113.
čen 09 00:25:04 hass avahi-daemon[280]: New relevant interface eth0.IPv4 for mDNS.
čen 09 00:25:04 hass avahi-daemon[280]: Registering new address record for 192.168.0.113 on eth0.IPv4.
čen 09 08:29:10 hass avahi-daemon[280]: Withdrawing address record for 192.168.0.113 on eth0.
čen 09 08:29:10 hass avahi-daemon[280]: Leaving mDNS multicast group on interface eth0.IPv4 with address 192.168.0.113.
čen 09 08:29:10 hass avahi-daemon[280]: Interface eth0.IPv4 no longer relevant for mDNS.