I am pretty sure the monarch can abdicate even after a coronation.
As far as the Queen’s power goes, I think the monarch has the technical authority to demand the Anglican Church do certain things. Just as the monarch technically has the power to, say, dismiss the parliament and not call it back again, to appoint and dismiss a Prime Minister, etc. The Queen could do all these things technically on her own, but realistically the moment she did so she would probably be deposed, forced to abdicate, and either another member of the royal family would be crowned as the monarch, or the Brits would just say sod it all, we are going to be a Republic. So if the Queen interferred directly in the movements of the Anglican Church, she would face the same consequences or just be completely ignored.
Basically the monarch’s authority in church matters boils down to approving whomever the Anglican clergy puts forward to be appointed bishops, etc. Same goes for the civil side, the monarch is consulted, signs all the laws, and appoints all the leadership, but basically this just means the monarch does whatever Parliament wants to do. You also have to consider that the Queen is the head of the entire Anglican Communion, so any change she made would affect loads of countries.
The idea behind the monarchy today is that in some apocalyptic scenario in which some crazy people tried to take over the country or something, the monarchy could get rid of them and appoint a new parliament in defense of democracy and English law. I personally think maybe it would have been better for the monarchy if it had exercised some of its powers on occasion through the centuries on key matters so that’s it had the actual power today to do something. For example, it might have been able to step in when the Anglican Communion decided to go all in on female priests, gay marriage, gender neutral bibles, and other things contradicted by all of Christian history.
Our Anglican and/or British friends should feel free to correct me of course.