I know there are other posts here asking this, but those suggestions do not help, the configuration keeps changing and I simply cannot get my own changes to persist.

I have the Google 8.8.8.8 and 8.8.4.4 servers in my Network Manager configuration in the GUI, and

systemd-resolv --status returns

Link 2 (enp38s0f1)

      Current Scopes: DNS    

DefaultRoute setting: yes    

       LLMNR setting: yes    

MulticastDNS setting: no     

  DNSOverTLS setting: no     

      DNSSEC setting: no     

    DNSSEC supported: no     

  Current DNS Server: 8.8.8.8

         DNS Servers: 8.8.8.8

                      8.8.4.4

          DNS Domain: ~.   

Nevertheless, dig google.com shows

;; Query time: 0 msec

;; SERVER: 192.168.1.1#53(192.168.1.1)

;; WHEN: Mon Oct 05 11:08:26 EDT 2020

;; MSG SIZE  rcvd: 83

so my default route 192.168.1.1 as DNS. Furthermore, /etc/resolv.conf is a symlink to /run/systemd/resolve/resolv.conf, which in turn reads

# Generated by dhcpcd from enp38s0f1.dhcp, wlp0s20f3.dhcp

# /etc/resolv.conf.head can replace this line

domain fios-router.home

nameserver 192.168.1.1

# /etc/resolv.conf.tail can replace this line

The only enp38s0f1.dhcp file on this system (I've searched /) is /run/dhcpcd/resolv.conf/enp38s0f1.dhcp, which reads

# Generated by dhcpcd from enp38s0f1.dhcp

domain fios-router.home

search fios-router.home

nameserver 192.168.1.1

I have tried to write in other nameservers there, but they do not persist. In the past I've made the changes persistent by making the file immutable with chattr +i, but

lsattr /run/dhcpcd/resolv.conf/enp38s0f1.dhcp

returns

lsattr: Inappropriate ioctl for device While reading flags on /run/dhcpcd/resolv.conf/enp38s0f1.dhcp

so that attribute is not available here. And besides, I shouldn't have to make the file immutable anyway: there should presumably be some way I can control the DNS server..

Edit:

In response to comments below:

$ dpkg -l *dnsmasq*

---

Desired=Unknown/Install/Remove/Purge/Hold

| Status=Not/Inst/Conf-files/Unpacked/halF-conf/Half-inst/trig-aWait/Trig-pend

|/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad)

||/ Name             Version         Architecture Description

+++-================-===============-============-============================================

un  dnsmasq          <none>          <none>       (no description available)

ii  dnsmasq-base     2.80-1.1ubuntu1 amd64        Small caching DNS proxy and DHCP/TFTP server

un  dnsmasq-base-lua <none>          <none>       (no description available)