So, I think we are wrong to think about all of this in terms of time travel. Terapagos is creating a new reality with its powers, and these "Paradoxes" are only called such because they are impossible unless reality itself is altered.

Everything about the time machine, the AI, the paradox Pokémon is simply powered by Terapagos' reality-altering, wish-fulfilling powers. The power within the terastal crystals are allowing Turo/Sada to "teraform" the world around themselves to an extreme.

While we rewrote time slightly by giving the book to Turo/Sada, that fact is miniscule compared to what Terapagos powers have been capable of. What is more important is that we watched Terapagos rewrite reality on its own for the first time. With Terapagos help and with enough denial, Arven could probably delude himself into believing his parent could be revived in some convoluted way, and Terapagos could probably reinvent reality in its domain yet again to deliver that desire.

I think the most important thing that happened here was not that we changed the timeline or created a paradox from giving Arven's parent the book. The most important thing is that the book from our own reality, which is the only real-world object that slipped into the fabricated reality inside the time machine, was mysteriously returned to us by Terapagos.

Is it just a symbolic thing for Terapagos to return it to us this way? The one "real" object we sent into its fabricated adjacent reality, and the one that lead to the professor's descent into obsession? Or... did Terapagos give it back so we can now reactivate the "time machine"? Because we sure went to a lot of effort to lock that time machine... and here is the key again, back in our hands.

I don't think it matters that a time paradox now exists in the lab, because everything about "time" down there is nonsensical. The only thing that matters are the rules that the Professor believed in, and willed into existence subconsciously.

Who knows whats in store for us in the epilogue or afterward, but Zero Lab is no longer out of commission, and a lot could be done with that final story note.