It seems to me that what you call "GM play" at T0 (assuming this is "prep time") is...not really "play" in any sense I would recognize. Indeed, it would seem most TTRPG players feel that way, since GM prep is considered a form of work, a duty the GM must fulfill--hence why so many take the position that the players owe something to the GM for their hard work. It may be joyful work, undertaken out of love or enthusiasm, but it is still work, rather than play proper.
I'm also confused because you seem to be presenting T0 and T2 as, essentially, identical things (since you use identical phrasing other than the word "Some" and changing "view" to "light"), but at least to my mind there are actually three different actions occurring here.
T0: GM does preparation work, which often involves both (if you like) "master map/key" construction and theatrical notes for the performance (NPC details, monster alignments, faction membership, etc.)
T1: GM and player actually interact, which is something we all unequivocally consider play on both sides.
T2: GM does wrap-up/tallying/etc. of the preceding events, ensuring sufficient notes are kept to support the next round of the cycle.
Both T0 and T2 don't strike me as "play" in a meaningful sense. They are a lot more like...well, a sort of "creative bookkeeping" (and not in the "cooking the books" sense, but in the sense of keeping-the-books regarding one's creative work.) If we're extending the concept of "play" to include these things, I'd really want to know why you consider it "play."