Hi all, I'm using ubuntu 20.04 on a raspberry pi (64bit version).  And the problem is still present.  My netplan:

root@rbpi3-002:/etc/netplan# cat /etc/resolv.conf
# This file is managed by man:systemd-resolved(8). Do not edit.
#
# This is a dynamic resolv.conf file for connecting local clients to the
# internal DNS stub resolver of systemd-resolved. This file lists all
# configured search domains.
#
# Run "resolvectl status" to see details about the uplink DNS servers
# currently in use.
#
# Third party programs must not access this file directly, but only through the
# symlink at /etc/resolv.conf. To manage man:resolv.conf(5) in a different way,
# replace this symlink by a static file or a different symlink.
#
# See man:systemd-resolved.service(8) for details about the supported modes of
# operation for /etc/resolv.conf.

nameserver 127.0.0.53
options edns0
search sismonda.local cpe.telecentro.net.ar
root@rbpi3-002:/etc/netplan# cat 50-cloud-init.yaml
# This file is generated from information provided by the datasource.  Changes
# to it will not persist across an instance reboot.  To disable cloud-init's
# network configuration capabilities, write a file
# /etc/cloud/cloud.cfg.d/99-disable-network-config.cfg with the following:
# network: {config: disabled}
network:
    version: 2
    ethernets:
        eth0:
            dhcp4: true
            dhcp6: false
            dhcp4-overrides:
                use-dns: false
            nameservers:
                search: [sismonda.local]
                addresses: [10.0.0.31,10.0.0.10,10.0.0.62]

The output of "systemd-resolve --status"

root@rbpi3-002:/etc/netplan# systemd-resolve --status
Global
       LLMNR setting: no
MulticastDNS setting: no
  DNSOverTLS setting: no
      DNSSEC setting: no
    DNSSEC supported: no
          DNSSEC NTA: 10.in-addr.arpa
                      16.172.in-addr.arpa
                      168.192.in-addr.arpa
                      17.172.in-addr.arpa
                      18.172.in-addr.arpa
                      19.172.in-addr.arpa
                      20.172.in-addr.arpa
                      21.172.in-addr.arpa
                      22.172.in-addr.arpa
                      23.172.in-addr.arpa
                      24.172.in-addr.arpa
                      25.172.in-addr.arpa
                      26.172.in-addr.arpa
                      27.172.in-addr.arpa
                      28.172.in-addr.arpa
                      29.172.in-addr.arpa
                      30.172.in-addr.arpa
                      31.172.in-addr.arpa
                      corp
                      d.f.ip6.arpa
                      home
                      internal
                      intranet
                      lan
                      local
                      private
                      test

Link 3 (wlan0)
      Current Scopes: none
DefaultRoute setting: no
       LLMNR setting: yes
MulticastDNS setting: no
  DNSOverTLS setting: no
      DNSSEC setting: no
    DNSSEC supported: no

Link 2 (eth0)
      Current Scopes: DNS
DefaultRoute setting: yes
       LLMNR setting: yes
MulticastDNS setting: no
  DNSOverTLS setting: no
      DNSSEC setting: no
    DNSSEC supported: no
         DNS Servers: 10.0.0.31
                      10.0.0.10
                      10.0.0.62
                      10.0.0.3
          DNS Domain: sismonda.local
                      cpe.telecentro.net.ar
root@rbpi3-002:/etc/netplan#


I found an extra dns and the domain search of my ISP!