The Monarch retains the power to veto any legislation, appoint/dismiss a Minister including the PM, prorogue/dismiss parliament as a whole, and technically all foreign relations treaties, declare war etc. but all this is done "on the advice of" a minister.

However, as an anti-monarchist I'd like to point out that for a couple centuries the Monarch has never once had a piece of legislation put before them that they felt the need to veto.

So how much power the Monarch retains is really a mystery, because it could be as simple as someone from the Monarch's office going "he ain't signing that" and instead of potentially introducing a constitutional crisis they torpedo the legislation.

The interesting thing to me is still how the Monarchy kowtowed to Trump, so given they have full authority to enter treaties/deals/pacts with foreign nations, what that could potentially entail.

In Australia, the Governor General is, constitutionally, the representative of the Crown, which the King is also. The GG in Australia can lawfully dissolve parliament under certain conditions, I think. Has been done in the past, anyway.

I expect that the King of the UK can dissolve parliament. But that's just a distant observer's speculation, of course.