For the thousand time - the Queen does not make policy or enforce laws or get Brits to testify in America. In that sense, she is merely a figurehead.
People like to tell themselves fairy tales to feel better. Let ‘em be.
So she has no pull whatsoever behind the scenes?
For the millionth time...the queen has no, none, zero, bupkiss, nada culpability nor influence in policy making in the UK !
She is a FIGUREHEAD, who performs CEREMONIAL procedures, such as the opening of Parliament, hosting foreign dignitaries ( a la STATE DINNERS ), opening flower shows at Kew, watching the TROOPING OF THE GUARD, supporting charities, laying wreaths on Armed Forces Day, etc.!
The Queen ( and in the recent past and again in the future, the KING ) also acts as a sort of "ambassador" to other nations; especially those that form the Commonwealth.
Even in the past, when the monarch still had a tiny bit of "power", it was nothing much to speak of and that has been the case since right after Cromwell.
The BIGGEST "job" of the Brit Royalty is to draw people TO the UK, as tourism is a large part of their economy.