No, that's not correct. The king of England has the right of Consent (as far as I understand, King's consent to bills is required), along with the veto right.
That's the idea of a functional constitutional monarchy: the long-reigning monarch counterweights the short-governing government.
> As far as I understand, King Charles exists for the purposes of being a tourist attraction, and has no power.
No, the monarchy has veto power over parliament, and has secretly used the threat of it to shape British law. Apparently most new legislation is run by the ruling monarch's office to make any changes they'd like before it hits the parliament floor for debate. https://www.theguardian.com/uk-news/2021/feb/08/royals-vette...
The Shah needed the military to help him remove the head of government in 1953. He was technically at the top, but really the prime minister held more power until the coup
King Charles has little actual power, but a ton of theoretical power. If he somehow convinced the military to back him (and he would probably need all of NATO's support) he could do whatever he wanted in the UK too.
