Welcome to the forum. While improvisation is certainly not the most popular sort of piano playing, here or elsewhere, those of us who engage in it regularly would assert the experience is one of the most profoundly satisfying in music. You are completely free to play any notes you choose in whatever way you choose, and this freedom carries with it the need to be yourself at all times. It is not something many trained pianists find at all comfortable, but once past the initial inhibition, the rewards of doing it over a lifetime are truly immense.
Your playing shows you have feeling for rhythm and phrase, a much rarer quality than one is likely to suppose. The "how" is much more important than the "what" when beginning to improvise, so don't fill your mind and impede your idea flow by concentrating too much on names and labels of scales or chords. Learn them in terms of your ear and the keyboard by all means, but then put them into your unconscious and whenever you improvise let your mind run free. Being able to get a flow going, with meaningful statements and ideas, is much more important than memorising a lot of note combinations. At seventy, I am not sure I know what an Am phrygian is. I possibly play it, but I don't clutter my creative brain with useless labels.
Structure and the lack of it are just creative options, theories are just creative options, the same as anything else in music. "Do what thou wilt shall be the whole of the law." Start from freedom and work towards an order of your own making over time. I hope we shall hear more from you soon.