The question stems from Philippians 2:6, YLT:
[Christ Jesus] who, being in the form of God, thought [it] not robbery to be equal to God,
The word English word 'form' is translated from the Greek word 'morphe'. Morphe unequivocally means form. I do not care how many word games one plays you will never get around the fact that 'morphe' means form. Saint Paul was writing to the Philippians who spoke Greek. So we can assume Saint Paul and the God who inspired him intended to use the word morphe with profundity.
Existence and form are two closely related concepts. Notice the wording of Philipians:
who, being in the form of God (YLT)
who, existing in the form of God (KJV)
who was in the form of God (NAB)
All objects have form and if they exist, if they are real, they certainly have a location. God meets these requirements. God has form. God is located in the discrete object known as Heaven. Heaven is detached or set apart from all objects of matter that is the atoms and the fundamental objects that mediate light and gravity to and from all atoms and which all atoms also derive their form from.
Form in this context refers to an intrinsic quality. It does not refer to an extrinsic quality such as appearance, look, color, etc. Form is a quality that is observer independent. Form is a quality that an object has of itself, independent of other objects or comparative relations. So God has a form independent of anyone in Heaven observing God. And God has a form prior to God creating all the objects in the set called matter. God's Form and Existence require Faith and a new language in order to understand.
What is form? Form is a term that relates what is bounded from an immediate surrounding. (Synonym: shape) Form is a delineation or demarcation which distinguishes an object from lack of form and other things. Form is an identifying distinction. Form distinguishes the referent from its surroundings. It is the inability for the entity to lose its border/outline and morph into its surroundings and disappear. Form implies some type of surface.
Truly God is bounded from His immediate surroundings. He has some type of singular face delineating Him from nothing as well as all other objects. If this were not the case God would be a pantheistic God. When the just are assumed into Heaven they do not spill into God, and God does not spill into them. Rather they are initiated into an immediate relationship with God within an real object called Heaven. They see Him face to face with no go bet-weens. Still God is bound from the environment of Angels and Saints in Heaven. Otherwise how could a face to face relation be possible? The Angels and Saints do not morph into God, and God does not morph into the Angels and Saints or atoms, trees, stars, etc.
Furthermore even when the Holy Spirit is sent and resides within a human, he still retains his unique form. He relates intimately to that human form, more so that any two humans can possibly relate but he retains his own form. Truly the Holy Spirit is superposed with the soul and body of a human in sanctifying grace and this is similar to how the mediators of light and gravity behave. And yet again in spite of this mystical superposition, He, the Spirit still retains his singular form.
What is the form of God? I don't know. God is not of atoms or the fundamental constituents of atoms. God has a supernatural, a miraculous form that transcends all atoms and the mediators of light and gravity between all atoms. He is not of the same stuff Angels are made of or human souls.
Perhaps God's form could be described as intensely Personal. The One God is Three: Tri-unity. There is the eternal generation. The Father eternally generates the Son; the Father and the Son eternally generate the Spirit. Clearly all Three have form and cannot possibly exist apart from one another, and there is no choice in this. Perhaps we could say the Three Divine Persons bind each other from their immediate surrounding. God delineates God: The Father is in Me and I am in the Father (John 14:11). The Father is fully God. The Son is fully God. The Spirit is fully God. The The Father is delineated from His immediate surroundings by the Son and by the Spirit. The Son is delineated from His immediate surroundings by the Father and by the Spirit. The Spirit is delineated from His immediate surroundings by the Father and by the Son. Blessed Anne Catherine Emmerich described God like a sphere within a sphere within a sphere. So there are Three Divine Forms yet One Divine Form. It is sort of like how all the fundamental subatomic objects converge and superpose to form a single atom. They are many, and yet one.
Of course one could also describe God's Form as living, immortal, eternal, almighty, holy, loving and so on and so forth, but until we can somehow see and relate the the Blessed Trinity in Heaven our concepts, although true, will always seem insufficient, unsatisfying, incomplete and so on.