Do I need to wait for a journal to "consent" to paper withdrawal before submitting elsewhere?
I'd recommend waiting a week or two to see whether you get a response to your withdrawal.  At this stage it can't be urgent to resubmit immediately, and having their reply would guarantee that they are aware that you have withdrawn the paper.  (By contrast, I don't think an e-mail read receipt means much.  For all you know, an administrative assistant opened the e-mail and then mistakenly deleted it without realizing what it said.)  I wouldn't go so far as to say you are required to wait for a response, but better safe than sorry.

I think you've got a much bigger issue to worry about, though, and that's why you withdrew the paper after acceptance.  At least in mathematics, withdrawing an accepted paper is extremely unusual.  To a first approximation, it typically means there's something seriously wrong with either the paper or the journal.  You can certainly do it, but given the effort that has gone into handling and refereeing the paper, you will cause offense if you don't have a very good reason.

If you inadvertently submitted the paper to a junk or predatory journal, then you don't need to worry about causing offense.  (Offending the editors of predatory journals is not a bad thing.)  In that case, withdrawing the paper is certainly the right decision.

If you dreadfully screwed up in your choice of journal, for example by submitting a brilliant breakthrough to a respectable but not impressive journal without realizing how good the paper was, then you should apologize profusely for wasting everyone's time.  Hopefully they'll understand that it was a genuine mistake on your part, and they'll sympathize with the awkward position you are in and give their blessing to resubmitting elsewhere.

If the paper is seriously flawed, then that's a respectable reason to withdraw it.  You might look bad for having submitted it, but then again, the referee didn't find the mistake either.  But this isn't a compelling reason to submit elsewhere soon: if you don't check whether the original journal is willing to publish the revised paper, then it looks like the changes were just an excuse to withdraw the paper.

Under normal circumstances, it will cause offense if people think you are withdrawing an accepted paper just to try your luck at a more prestigious journal.  In particular, this is a dangerous impression to leave if you ever hope to submit to this journal again.  As an editor, I would certainly not be happy to see a new submission from an author who had previously withdrawn an accepted paper without a compelling excuse.

All this gives you another reason to move slowly and wait for a reply.  If you have a good reason for withdrawal, then it's worth making sure you have communicated it clearly.  In any case, you are doing something rather unusual and serious, and it's best not to give the impression you are treating it lightly or casually.