Thank you for spending your time. Yes, resolvectl status's output is like yours in Global part, but in the end of the output there is this:
Link 3 (wlp3s0)
Current Scopes: DNS LLMNR/IPv4 LLMNR/IPv6 mDNS/IPv4 mDNS/IPv6
Protocols: +DefaultRoute +LLMNR +mDNS -DNSOverTLS DNSSEC=no/unsupported
Current DNS Server: 192.168.1.1
DNS Servers: 192.168.1.1
Default Route: yes
As you see, wlp3s0 uses the default ISP DNS. Wireshark's output confirms this.
I ran the command with sudo and got the error. I created the file with sudoedit and added the contents in it and systemctl reload systemd-resolved. But the DNS requests are sent with port 53 to the default DNS server yet and:
cat /etc/resolv.conf
# This is /run/systemd/resolve/resolv.conf managed by man:systemd-resolved(8).
# Do not edit.
#
# This file might be symlinked as /etc/resolv.conf. If you're looking at
# /etc/resolv.conf and seeing this text, you have followed the symlink.
#
# This is a dynamic resolv.conf file for connecting local clients directly to
# all known uplink DNS servers. This file lists all configured search domains.
#
# Third party programs should typically 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 127.0.0.1
nameserver 192.168.1.1
search .
After updating
freedesktop.Platform
with flathub the problem has been solved.