I don’t really think it’s true either, but it would just be interesting. One thing it would explain is why she would give such a powerful and potentially destructive object as a time turner to a third year student. Otherwise, it’s just how strait laced, academic, and stern they both are whilst both having a potential to step outside the line when needed.
Certain spells and potions can be used to share a person’s essence onto the painted canvas so that a portrait is alive and can interactive with viewers. Does that mean, technically speaking, they function as more ethically created horcruxes?
No, the real person is still completely gone. It's more of a copy of the person. Think of it as an AI program. You could code it to look like a real person, and interact with you as they would. But the person it was molded on wouldn't be "connected" to it in any way. If I had an digital AI version of myself made, it wouldn't save me in any way from dying. It would just allow those I left behind to communicate with a copy of me.
Did Sirius ever get petted by anyone