I see when “root” user is required it is probably easier to install it rpm-ostree layer then using containers.
I did the following:
# Installed Wireshark in rpm-ostree layer
rpm-ostree install wireshark
# Rebooted to make affect.
systemctl reboot
# Add user to group as suggested by Timothée Ravier
grep -E '^wireshark:' /usr/lib/group | sudo tee -a /etc/group
sudo usermod -aG wireshark $USER
# Reboot to take user to group affect (maybe logoff is enough)
systemctl reboot
# Start program
wireshark
Now I see network traffic is visible to Wireshark and so problem solved.
Thanks for help.