The President is the head of the Executive Branch. He can give orders to the people who work for them as long as they do not violate law. So, yes, Executive Orders like that are perfectly legal.
However, at some point (probably in the early 1900s. maybe even earlier) the President’s got it in their head that they could issue edicts regarding federal lands, and other activities with which the executive branch agencies were responsible for, that went further than informing his own people how to do their job within the law. They decided that they could issue orders that then were binding on the public, and proscribe penalties and action if citizens did not comply. In essence, they decided they could make law. Any such Executive Order or Presidential Proclamation, unless specifically allowed by the legislature within an Act of Congress, is unconstitutional and illegal.
And, in as much as congress cedes its constitutional power to the President, without a constitutional amendment to that effect, that too is unconstitutional.
Such EO and PDs are not legal and are unconstitutional. Sadly, that is what he majority of them are directed at these days, and both Democratic and Republican Presidents are guilty of it.
The alphabet agencies that they created to avoid being blamed for the evil things they wanted done, are an even worse problem.