Yes, indeed if in fact, a Democrat, CR was voted on in the Senate and passed the Senate. It would then have to return to the house because the current version of the CR is a Republican CR passed in the house and referred to the Senate for affirmation.
You’re correct this is not fake news. This is a hypothetical that has not occurred. The only CR currently before the Senate for vote because it is controlled by soon is the one referred to the Senate by the house Republicans and smattering of Democrats.
It is a shame that some people haven’t the notion of what you’re talking about
Well technically if it added anything, such as an extension of the subsidies, it would not be a CR any more. It would then be a new appropriation bill. A CR is a temporary agreement to continue to operate the government under the existing appropriation bill. Adding new appropriations makes it an appropriation bill.
This is more than just semantics, or at least it is if we are still following the Constitution. The Senate could not vote on such a bill and send it to the House. All appropriation bills must originate in the House, so presumably that would apply to this hypothetical bill.