"No DNS servers known" in /run/systemd/resolve/resolv.conf

1) The release of Ubuntu you are using, via 'lsb_release -rd' or System -> About Ubuntu
Description: Ubuntu 20.04.3 LTS
Release: 20.04

2) The version of the package you are using, via 'apt-cache policy pkgname' or by checking in Software Center
systemd:
  Installed: 245.4-4ubuntu3.13
  Candidate: 245.4-4ubuntu3.13

3) What you expected to happen

/etc/network/interfaces:

auto lo
iface lo inet loopback
    dns-nameservers 1.1.1.1 8.8.8.8

auto eth0
iface eth0 inet static
    address ip/24
    mtu 1500
    post-up route add default gw gw_ip || true
    pre-down route del default gw gw_ip || true

When system rebooted I expected in

/run/resolvconf/resolv.conf:
nameserver 1.1.1.1
nameserver 8.8.8.8
nameserver 127.0.0.53

and in /run/systemd/resolve/resolv.conf:
nameserver 1.1.1.1
nameserver 8.8.8.8

This is stated in "man 8 systemd-resolved":
systemd-resolved maintains the /run/systemd/resolve/resolv.conf file for compatibility with traditional Linux programs

4) What happened instead

/run/systemd/resolve/resolv.conf:
# No DNS servers known.

But after restarting systemd-resolved it update this file correctly.

5) Also

The system behaves correctly when DHCP is used. So when in /etc/network/interfaces:
auto lo
iface lo inet loopback
auto eth0
iface eth0 inet dhcp

Then /run/systemd/resolve/resolv.conf updated correctly straight without restart.