Pi-hole DNS service not running after first install

It's good dnsmasq is inactive - that means it's currently not interfering with Pi-hole.

It still could be restarted on rebooting your machine, so it's probably best to remove it completely:

sudo apt-get purge dnsmasq

As you don't use the Google kit anymore, you could just delete /etc/dnsmasq.d/googadget-dnsmasq.conf.
If you want to backup it instead, don't keep it in the dnsmasq.d/ folder by just renaming it - move it away, e.g. to your home directory.

Then restart Pi-hole by running:

pihole restartdns

As to what happened:
That left-over configuration under dnsmasq.d/ instructed pihole-FTL to start its DHCP server and propagate itself as router (option 3) and DNS server (option 6) for devices on usb0.
In doing so, Pi-hole also tried to access the standard lease file, which likely was created by your Google kit sometime before, hence the permission mismatch.

Removing the configuration file will allow Pi-hole to operate as expected.
Purging dnsmasq from your system will ensure pihole-FTL and dnsmasq won't fight over port 53.

Your own take at setting permissions for that non-standard Pi-hole file may have worked for the moment, but it didn't address the root cause at all.