global-dns not working

[AP <gnome inml grue cc>]

Hi,

Using NM 1.20.0 with Debian Buster (though this also happens with 1.14.6) and am
trying to get the global-dns section to work so that I don't have to type it in
for each and every connection I create.

Alas, it's proving to be a pain and not doing what I want (ie working at all). The
config, as NM sees it is as follows:

--- 8< ---
Read config: /etc/NetworkManager/NetworkManager.conf (lib: no-mac-addr-change.conf) (etc: dns-resolv.conf, 
min-systemd.conf)
CONFIG: config-data[0x55b3773e11b0]: 5 groups
CONFIG:
CONFIG: [main]
CONFIG:   plugins=ifupdown,keyfile
CONFIG:   dns=default
CONFIG:   rc-manager=symlink
CONFIG:   systemd-resolved=false
CONFIG:
CONFIG: [global-dns]
CONFIG:   searches=moo.cow
CONFIG:   options=edns0
CONFIG:
CONFIG: [ifupdown]
CONFIG:   managed=false
CONFIG:
CONFIG: [logging]
CONFIG:   level=TRACE
CONFIG:   domains=ALL
CONFIG:
CONFIG: [device-mac-addr-change-wifi]
CONFIG:   
match-device=driver:rtl8723bs,driver:rtl8189es,driver:r8188eu,driver:8188eu,driver:eagle_sdio,driver:wl
CONFIG:   wifi.scan-rand-mac-address=no
config: state: successfully read state file "/var/lib/NetworkManager/NetworkManager.state"
...
dbus-object[95d2215dc96192ea]: export: "/org/freedesktop/NetworkManager/Settings/2"
++ connection 'new connection' (0x55b377439940/NMSimpleConnection/"802-11-wireless"): 
[/org/freedesktop/NetworkManager/Settings/2]
++ connection                [ 0x55b377422420 ]
++ connection.id             = 'Bob'
++ connection.permissions    = []
++ connection.type           = '802-11-wireless'
++ connection.uuid           = '1f0df990-cf4f-49a4-8f53-3ce9b188630c'
++ 802-11-wireless           [ 0x55b3773f5130 ]
++ 802-11-wireless.mac-address = '01:23:45:67:89:ab'
++ 802-11-wireless.mac-address-blacklist = []
++ 802-11-wireless.mode      = 'infrastructure'
++ 802-11-wireless.ssid      = ((GBytes*) 0x55b37742aa90)
++ 802-11-wireless-security  [ 0x55b3773e13d0 ]
++ 802-11-wireless-security.auth-alg = 'open'
++ 802-11-wireless-security.key-mgmt = 'wpa-psk'
++ 802-11-wireless-security.psk = ****
++ ipv4                      [ 0x55b3773e1490 ]
++ ipv4.addresses            = ((GPtrArray*) 0x55b377439580)
++ ipv4.dns                  = []
++ ipv4.dns-search           = []
++ ipv4.method               = 'auto'
++ ipv4.routes               = ((GPtrArray*) 0x55b3774398e0)
++ ipv4.routing-rules        = <unknown>
++ ipv6                      [ 0x55b3774224f0 ]
++ ipv6.addresses            = ((GPtrArray*) 0x55b37743f900)
++ ipv6.dns                  = []
++ ipv6.dns-search           = []
++ ipv6.method               = 'auto'
++ ipv6.routes               = ((GPtrArray*) 0x55b3774482c0)
++ ipv6.routing-rules        = <unknown>
--- 8< ---

I'm attaching to a wireless access point (those config NM sees as per above) and
getting an IP via DHCP. IPv4 only.

Am I doing something wrong or is NM broken here? It's driving me a little crazy
as this SHOULD be simple (and appears to be simple).

Thanks.