NetworkManager not updating /var/run/networkmanager/resolv.conf

No wonder I said "Something is wrong here". In your "customization", you've kind of made an unnecessary mess of things. Stop trying to defeat the system. Sorry.

In /etc/netplan/*.yaml you've combined NetworkManager and netplan script. Your .yaml file should look like this...

network:
  version: 2
  renderer: NetworkManager

This information belongs in NetworkManager GUI connection profile, or in /etc/network/interfaces, in NetworkManager speak... not netplan speak...

ethernets:
    eth0:
      addresses: [192.168.0.11/24, 192.168.0.10/24] (why two addresses?)
      gateway4: 192.168.0.1

• reinstall resolvconf
• reset /etc/resolv.conf symlink
  • see below for link information
  • and don't manually edit this file
• edit /etc/systemd/resolved.conf (see below for instructions)
• remove dns=dnsmasq from /etc/network/interfaces
• remove dnsmasq* unless you can explain why you need it

Regarding dnsmasq and systemd-resolved...

Do a ps auxc | grep -i dns and ps auxc | grep -i resolv and look for dnsmasq and systemd-resolved, and if both are running, you need to disable the DNS part of systemd-resolved by editing /etc/systemd/resolved.conf and...

change:

#DNSStubListener=yes

to:

DNSStubListener=no

then restart systemd-resolve and dnsmasq, or reboot.

You MAY need to reset the symlink that is /etc/resolv.conf (if dnsmasq is not running)...

sudo mv /etc/resolv.conf /etc/resolv.conf.OLD # save the old symlink

sudo ln -s /run/systemd/resolve/resolv.conf /etc/resolv.conf # create new symlink

Note: original symlink is...

sudo ln -s /run/resolvconf/resolv.conf /etc/resolv.conf