I mean, by Pen's request and the words on TV's screen, TV was truly scanning the timeline's many years of history to process every bit to find any abnormalities within the timeline that contradicted the timeline to his knowledge, and for him to actually detect these abnormalities, he would have to see every bit that happened within that point in time in the universe, would he not? Even if he was only looking at the show's past history since 2008 up until now, he'd still need to process every bit of the infinitely-sized universe to find something off.
Here's what I see: After the characters obtained acausality, Pen looked into a thought bubble depicting TV depicting Taco doing the dance that was originally done by Flower did in
BFB 25, and Pen realized past events are changed from how he remembered them, including when they are viewed in TV's recordings. Pen then asked TV to scan their past to detect the failed debuters. TV was capable of doing this because he backed up footage of the
BFDI cartoon series and screenshots of the
BFDI prequel comics, which he was able to organize into a timeline infographic that labels only
BFDI material. After scanning the
BFDI timeline, it turns out the failed debuters were all participating in on-screen past events of
BFDI, so due to TV having saved all that footage that was being altered in accordance with the past getting altered, he was able to view the failed debuters. It's not as though TV had a clairvoyant view of the past, it just felt like that because he collected that much footage and the changes to the past must've also been saved by his past self before he obtained acausality.
So, no, TV didn't have to process every bit that happened within the points in time in the universe he scanned. He had to process the entirety of the vast footage he has collected of the entire series, which was already recorded, and there was no certainty that the failed debuters were going to be found until they were found due to having went to scenes in the past TV had saved footage of. TV has super intelligence and he had all the footage of failed debuters causing changes to the past, so he had all the information he needed to be capable of making a conclusion about temporality without having to empirically view the entire universe. This is a feat supporting Extraordinary Genius intelligence. Besides, how is my interpretation less likely than TV suddenly proving he basically has the superpower of cosmic awareness? The idea that TV made calculations based on the information he is already proven to have makes a lot more sense than the idea that TV suddenly proved he can see across infinite space and the temporal axis, especially when
TV has been caught off guard, like when Tennis Ball and Fourse accidentally fell on him. Even if TV can see literally everything and scan the setting's metaphysical timeline rather than the series' logged timeline, it's a specific activated ability, not something he passively does, which solves the inconsistency of characters being established to act in finite speed.
To be fair to you, I want to point out that it was also stated in the rapidly changing text during the "scanning timeline" process that TV was "calibrating universes" and "geolocating Earth," so I see how you believe TV was getting an outer space view if you were referring to those lines of text. To further defend my position I wrote in the previous paragraphs: The former quoted text probably means he was evaluating the original
BFDI timeline and the changed one to contrast them and detect anomalies, having called the different timelines "universes" because they really are different realities in a sense, and the latter quoted text probably means he's connecting to something like Google Maps to have an even easier time visualizing. Among those rapidly changing lines of text, TV was also downloading software and connecting to external servers, so the timeline scanning process is not as simple as TV just looking with his eyes, making is questionable to scale it to his usual perception speed. I suppose it's fine to call it possibly Infinite upon activation (based on the possible implication that TV had an outer space view).
If it was just insanely good stealth mastery as opposed to greater speed, then she shouldn't have gone in front of the contestants multiple times while rearranging them, and yet she does so at a sheer speed fast enough for them (Including TV) to not notice her even when she goes directly in front of them. That team swap scene is just too crucial of a plot point to ignore, especially when it's meant to showcase the powerful traits of Algebraliens that make them superior to the contestants that fits within the narrative of the series.
I was also thinking that Two and Four are potentially holding back just to have fun with the contestants (Especially the latter) which is why they seemingly don't blitz them and let them run, but then that would end up contradicting the entire plot of TPOT 11 that had the EXITors escape Four as the latter was very eager to keep them in the EXIT which would mean he wasn't holding back in that episode. Perhaps this one instance of the EXITors getting away from Four is simply an outlier for the former?
Like I said, I'm always up to applying a "possibly/likely Infinite" speed rating for One, Two, and Four if we can't be sure that they solidly scale due to inconsistencies despite the narrative indicating that they are more powerful than the contestants.
I guess that makes more sense. Four was outsmarted a lot in
TPOT 11 if I recall correctly, so that's probably intended to be the main reason the EXITors got away, and we can say they took advantage of Four being bad at using his higher speed at the right times. I agree with the idea that Four and Two restrain their full capabilities. Both of them want challenges to be interesting, Four often prefers to cause pain than instant death, and Two comes off as respectful despite them having the means to be as cruel as Four if they really wanted to. As for Donut kicking One, I guess that's the real outlier, for now, or maybe One was just that confident in her ability to convince people to accept her deals. If TV's usual perception speed is Infinite, then I think with this method it's fine to rate One, Two, and Four as likely having Infinite speed.
By the way, back when I made the Black Hole Reaches Infinity upgrade, I had considered making the proposal of scaling the feat's Infinite speed to the reality warping of Four and Two rather than only the feat's power, because the ability to "do anything" in this series would include replicating Black Hole being able to absorb across an infinite distance, but I decided to not bring that up because speed doesn't really have to do with the potency of reality warping and people were a bit skeptical of if Four and Two should even get the feat's power scaled to their reality warping anyway. Since you're taking interest in rating Four and Two that fast for a similar reason, I'm bringing this up just because you might find it useful. With this method, it might not even matter whether or not TV's scanning timeline speed is applicable to his usual perception or not, in the case that it's Infinite by any means.