He doesn't have any authority, in practice. It has been that way since 1414. The second the monarchy tried to exert control over politics would be the second it was abolished.
[1] - https://www.theguardian.com/commentisfree/2021/feb/08/queen-...
They were later "de-arrested," but the intended message is pretty clear.
Or you can point to things like the Kerr Sacking (in Australia, but using (vice-)regal power) and say it's not quite done yet, though in decline for centuries...