It is a constitutional monarchy with an elected, time-limited king.
Monarchies generally have (and had) lots of checks on the king's power. Not necessarily the kinds of checks we would like, of course. The rights of the nobility were well-protected, the rights of landless commoners were not.
Executive orders are memos, not laws. The President has no power for legislation or budget or tariffing. We're supposed to require legislative review of any emergency actions, like using the military.
> It is a constitutional monarchy with an elected, time-limited king.
> Constitutional monarchy, also known as limited monarchy, parliamentary monarchy or democratic monarchy, is a form of monarchy in which the monarch exercises their authority in accordance with a constitution and is not alone in making decisions.[1][2][3] Constitutional monarchies differ from absolute monarchies (in which a monarch is the only decision-maker) in that they are bound to exercise powers and authorities within limits prescribed by an established legal framework. A constitutional monarch in a parliamentary democracy is a hereditary symbolic head of state (who may be an emperor, king or queen, prince or grand duke) who mainly performs representative and civic roles but does not exercise executive or policy-making power.[4]
This is largely but not entirely true. It's also largely true by convention/Realpolitik ("try and exercise your powers and see how long you stay king!") and not by law.
> absolute monarchies (in which a monarch is the only decision-maker)
The monarch was essentially never the only decision maker in absolute monarchies. Nominally, yes. In practice, not at all. Going against too many established interested was seriously bad for the monarch's health.