While there is no Executive Order, there is still an identifiable policy that has been formally adopted and justified on the basis of "prosecutorial discretion".
The case will hinge on whether "prosecutorial discretion" can be used to justify a broad policy of non-deportation of millions of illegals or whether it's applicability is limited to selected case-by-case decisions.
In other words, is the President violating his oath to "faithfully execute the laws" or is he justified in applying "discretion"?
It seems to me, but perhaps I am wrong, that courts have already decided that he can enforce whtever law he wants and however he wants to enofrce them.
Because he has clearly not been faithfully executing laws, and he has never been held accountable for that, in fact in a number of instances, he has been changing laws at will, which he clearly has no authority to do, and he hasn’t been held acocuntable for that either by either a court or by the people who allegedly write those laws.
A second question is whether he can affirmatively provide them with IDs and legal status even if he has the power to not prosecute based on "prosecutorial discretion". One is a non-action which can be rationalized (I won't say justified) by a finite budget and a much larger pool of violations which could be prosecuted. The other is an action which requires that he spend money that hasn't been appropriated for that function.