What is the math behind the profile's "Fleet Power"

Tl;DR: The fatal flaw in your attempts to find a formula is that you assume a linear function. The function is most likely based on c * sqrt(X), where X is total stats of your fleet and c is some arbitrary constant chosen by the developer.

Long answer: I started playing less than two weeks ago, so I have a new account where I can do some low-end testing. I am currently much closer to ~1FP for every ~60 total stats; raising a ship's power by ~230 will give me 3-4 Fleet Power. On the other hand, if I look at the leaderboards, the top ranked players have only about 6x as much Fleet Power as me (12000 vs. 2000), but I'd expect their total stats to be at least 20 times as high as mine.

On a side note, moving all the gear from my strongest to my weakest destroyer (after stripping the weaker one down) had no effect on my Fleet Power. Javelin went from 3191 to 2039 Power (-1152), Cygnet went from 672 to 1824 (+1152), and my Fleet power remained at 2066. Dismissing duplicate ships has no effect, and neither does collecting or powering up Collab ships.

The obvious conclusion is that, the higher your total stats already are, the more stats you have to gain to increase your fleet power. This assumption should explain all the observations in your data, e.g. a new ship giving 6-7 Fleet Power early on and only 2 Fleet Power later on.

The developers have a simple reason for doing this: Making the leaderboards look less intimidating for new players and giving them the illusion that they might be able to catch up. On the other hand, there would be no reason for the devs to calculate all the different variables you gathered and plugging them into a formula.

This is an interesting post and I actually found it while trying to find more info on collab ships on fleet power as my testing showed they do not have any impact and based on some replies here it only confirms that. I'll have to check how it goes with the -chan ships (EDIT: -chan ships actually contribute to fleet power, just tested) but I suspect it's the same story, likely only ships that count towards fleet tech contribute to fleet power. I only realized it this collab which is kinda uh oh since I'm trying to maximize fleet power basically since the game launched (and I'm currently the #1 AL EN fleet power rank). But better late than never.

One thing I can add is that multiple copies of ship do not count at the same lb level. However different stages of LB will each contribute to FP. So to max fleet power you will need 4 copies of each ship at 4 different LB levels. In other words 11 copies of each ship (or bulin combinations), 1, 1+1, 1+2, 1+4.

Another factor that contributes to FP are the bonuses from fleet tech.