Yes, but it does not make sense.
Yeah I think it is too much 
will try the adguard dns
You could register adguard dns for free and put your address in your router or any devices. My screenshot blurred because it is my own control dns in adguard dns server.
I know confuse between Adguard dns server and Adguard home (Local dns server).
Adguard DNS
Another way you could use Cloudflare (1.1.1.1) or Google (8.8.8.8)…
Why not use the Adguard Home instead of adguard dns since you have full control over it
Adguard DNS servers with their own blocklists have other advantages, as they work without a router if you want them to.
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When you type Google.com and Adguard dns server looking Google’s IP to go your Adguard Home. Local computer type Google.com from Adguard Home.
If empty upstream in your AdGuard Home then local dns can’t find Google’s IP address or any websites. That why your PC wrote local dns IP from DHCP.
Type your PC ipconfig /all and what you see dns IP address?
You can use custom Adguard DNS server on your mobile with 4G/5G like @admon said.
How about setup all the devices to default or no private dns, since the router will handle all the upstream DNS server request… it is the same right?
Here my Adguard DNS server and I made things. You noticed my router (traditional router + home assistant with Adguard Home) has zero blocked, because Adguard Home blocked first.
Next I used private DNS on my phone for outside network - 3G/4G/5G.
Travel router is new router for travel (Beryl Ax which inside Adguard Home).
hope understand how is working 
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You could make quad dns, google dns, Cloudflare, Adguard dns server, just make each line and listen upstream random. You could test dns leak website and you will notice different results when you refresg page
Imma try that adguard dns, as of now I am using a third-party VPN with a quad9 private dns server.
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I had a similar problem with adguard. It was going to Amsterdam instaed of London. When I chnaged to IP6 server it is now going to London
