I think a clinical psych person may label this as depersonalization/derealization.
But I like how the parent called it "a slow integration of diverse parallel processes" - not labeling the experience as some kind of problem.
I think they mean the strong sense of déjà vu. I get a weird one where the déjà vu itself is what I've felt before, déjà vu squared. Feels horrible!
Yes! I've experienced this a few times before, like a meta-déjà vu. It is a really uncomfortable feeling.
Description sounds like normal déjà vu to me. It's not a feeling that I felt before, it's a feeling that I know what's going to happen the next moment, but I can't actually recall it, but the moment it happens I recognize it as recalled.
Sometimes, I feel like not only I've been in this same situation before and know what will happen next, but also that I've felt like I've been in this same situation before. So basically like this is (at least) the third time I'm experiencing this situation: once when it was new to me, a second time where it felt like deja vu, and this third time where the deja vu itself is already familiar.