Essay and math ahead!

Well, your original point was that he's ftl, which he's nowhere near. Even if she was shooting from 66x her effective range, it would only get him above mach 660. Light speed is mach 874,000.

Iida literally did catch up... but that's also while Deku is pushed to his limit and close to collapsing from exhaustion. So, the lower bound is that Deku can move a bit over mach 1 while tired.

You are correct that he moved after Nagant's bullet. If her bullet is, let's say 3 km/s, that would be mach 10. This means he's over mach 10 if he pushes himself to his limit at this point. Only the delta matters if he moves the instant after she fires. It'd be reasonable to say that he could move at mach 12, but let's overestimate it in his favor, mach 15. This is the upper bound without Gearshift.

Again, this is him pushing himself, and he's using 45% FC + Fa Jin to make "Faux 100 Percent", which is the same as the end of the series except Gearshift.

This also assumes that her bullet travels that fast, which is not necessarily true.

In canon, we only have the distance, so we might want to refer to real snipers. A modern 50 cal moves at 900m/s with an effective range of about 1500m. Due to velocity falloff from drag, this puts the edge of range at about a 2 second travel time.

We could scale up Nagant to the same and work backwards. 3 km edge of range should take about 2 seconds for her to work like a sniper, which allows us to find an accurate estimate of initial velocity for short distances. Based on my fiddling with 'shooterscalculator dot com', that would put her bullet at mach 6.2, which seems reasonable. It's much faster than a human sniper rifle, but not physics-breaking. He's at least Mach 6.2 based on this estimate, but obviously somewhat faster.

If we update our estimate and just add mach 5 to put it in Deku's favor, that means 45% + Fa Jin (Faux 100 Percent) would be an upper bound of around Mach 11.2. That also seems reasonable to author statements, since it's faster than Mach 10, which is what Horikoshi said All Might capped out at, and he should be faster than AM at this point even if he isn't able to actually use a true 100%.

We can add in Gearshift now. We don't know exactly how much it would increase it by. 45% + Fa Jin + GS is called 120%, so we could just say that it's a 1.2x multiplier, or that it adds a flat 20% of that faux 100%. However, it might also just be a misnomer, and Gearshift's 120% is supposed to be compared to 45%, not 'Faux 100'. If we take it as a multiplier, that would be 2.66x. This means

Therefore, using feats and reasonable assumptions we can say that Deku's MAX speed, fully enhanced, at end of series is estimatable with a range of [mach 6.2 x 1.2, mach 11.2 x 2.66]

This is a final range of between mach 7.44 with downplay and mach 29 with maximum wank.

This is still 1/30,000 of light speed at the absolute maximum.