Usually pretty good support from Dreamhost in my experience, but I’d put those back soonest.
In the dreamhost control panel there are usually A records for the domains, if you use those instead is there any difference?
For fun you can point one of your domains to httpbin.org. If it gets redirected there it should show you the host header being sent. If it doesn’t get redirected and instead goes to the main website, review all the places linked above again because there’s a rule on Cloudflare making a redirection or header rewrite somewhere.
If you go to https://test.demo.dog/headers you’ll see that one of the headers in the response is host and it matches the host name in that URL which is good (the right thing). And since you just hit the page it probably will for you as well, but doublecheck by adding /headers to the URL for your domain to confirm. If it does match then I’d recommend the A record path just to be sure you’re pointed to the right origin server or service at dreamhost if that’s what’s in your DNS control panel (actually doublecheck that what you have entered matches regardless).
You can also the records to eliminate Cloudflare completely from the equation (beyond DNS resolution of course).