Apple Private Relay: With or without DNS

I've got a difference between DNS settings and also would like to find out if this happens to others. And what is the correct behaviour.

In my network settings the DNS section tells me this:

DNS requests are being routed by iCloud Private Relay for this network. Turn off Private Relay to manually configure DNS settings.

I have an iMac and a MacBook Air.

In the iMac I have Safari and Firefox.

If I don't set any DNS server then Safari still works. I can browse the internet and listen to music. But Firefox doesn't work. It says cannot find page. (Is this normal on Private Relay? No DNS setting but Safari still works?) If I put DNS setting then Firefox works. As expected of course.

But:

In my MacBook Air (I only use Safari in this MacBook Air) If there is no DNS setting then internet pages can't connect. If I set a DNS server then internet works.

So:

I don't get the correct behaviour. Because if I don't set DNS in the iMac then internet works. But if I don't set DNS on my MacBook Air then internet doesn't work. I expect that as the Relay routes then I don't need DNS settings in both machines.

What is the correct behaviour? Do I need to set DNS or not for Private Relay? Might be a bug? Or maybe I'm just missing something?

The difference between my two machines is that the iMac (M1) is on Ethernet cable and MacBook Air (M2) is on Wi-Fi.

Both on Monterey.

Anyone who takes the time to read this and gives any insight, my thanks in advance.