"The actual thing that the debt ceiling does is stop the Treasury from issuing debt to pay for things Congress has already decided to pay for."
It's unlikely it does that. If it came to a court the judge would have to decide which of Congress's instructions take precedence or how to reconcile them. That falls into territory of implied repeal and reinterpretation of the Federal Reserve Act.
If the Democrats had any backbone, they would instruct the Fed to pay what Congress has authorised and if the Fed said 'no', take them to court to force an interpretative judgement to settle the matter. (which I call the 'empty chest' problem).
Which would almost certainly involve reading section 15(1) of the Federal Reserve Act using the same 'futurity' that the courts have used in appropriation bills.
(ie the deposits it talks about are past, present and future deposits).
That would imply a balancing amount held at the Fed, and the debt ceiling stops the Treasury refinancing that balance into bonds.
Both the spending and the debt ceiling requirements of Congress are then satisfied - and the tool is neutered.