Wait, are you saying that if foo.example.com and bar.example.com are each CNAME records pointing at example.com (and the server has regular name based vhosts to isolate what is served for each), then browsers use a single cookie jar for foo and bar? So if the admin of the foo site and the admin of the bar site are adversarial, they can steal each other's cookies?
That doesn't seem right at all... I hope I am misunderstanding.
Now, if the admin of foo overrides the cookie scope to be *.example.com instead of the default foo.example.com, then yes it's expected that the admin of bar can steal foo's cookies. This is mentioned in the NextDNS Medium article you linked to, toward the end. This is definitely a "gotcha" situation but at least the default is safe, as far as I can tell.