This answer from 2017 on whether the Queen could have stopped Brexit states (emphasis mine):
Furthermore, the executive power of the British government to make and withdraw from international treaties is a royal prerogative, exercised on the Queen's behalf by the Prime Minister and Cabinet. If the Queen saw fit, then in theory she could use these powers herself. French President Macron has suggested the UK could choose to remain in the EU; the Queen could simply declare that she is exercising this option and cancelling Brexit by royal decree.
The rest of that answer points out that it would be entirely unprecedented for a modern monarch to act without/against the advice of her ministers, and concludes that
Unless the country was in such a state of crisis that it amounted to imminent or actual civil war, it is almost unimaginable that the Queen would interfere in politics in this way; or that the government, Parliament, and public opinion would tolerate such interference if she tried.
In light of the fact that none of the eight proposals on the table got a majority to support them, including a "we didn't work it out, so cancel the withdrawal" option, the UK is left with no clear path forward. I'm sure that there will be more negotiation, and more votes in the near future, but for the purposes of this question, assume that all votes fail to pass, and it is now April 11th (the day before the EU kicks out the UK).
Given all the various court rulings and votes that have taken place since that answer, I'm wondering if the Queen can still cancel Brexit. Does she still technically have the power to do so, as part of her heretofore unused executive power, or was it only the ability to object to the initial vote? Would the EU recognize an Article 50 withdrawal issued by the Queen instead of the PM?