What happens if I buy the Battle Pass at level 100 (using the in-game obtained V-Bucks)?

I am a Fortnite Italian player, who's been playing Fortnite for months, since summer 2019, and in this sense I'm a bit of a young player, since we are currently in the twelfth season, the 2nd of Chapter 2. I'm not going to spend any money for Fortnite, but I would like to get the Batte Pass someday, just using the V-Bucks that I get in the game, as I've always (and now I still do) got the rewards from the free battle pass, not being a premium player.

So far, in my 8 months of free Fortnite, I've earned 800 V-Bucks, and now I'm a level 21 player. At the level 63 and 99 of this season I'll get another 100 V-Buck reward, so totally when I'll be at level 100 I'll reach the good number of 1000 V-Bucks and since the Premium Battle Pass requires 950 of them, I'll be able to get it.

My question is: when in this season I'll reach level 100, and at that point I'll buy the Battle Pass spending 950 V-Bucks, am I gonna get all the Premium Battle Pass rewards of all the previous levels < (and equal to) 100?

In this way, I think, I'd get all the rewards of the season that I didn't get in my Free Battle Pass gaming period, that is, all the rewards excluding the Free rewards, that is, the Premium rewards. This means that I'd get also the 1500-300= 1200 V-Bucks of the Premium Rewards (since the totality is 1500 of them and the Free Battle Pass V-Bucks are 300), and so in this way I could get straight buy the Premium Battle Pass of the next season that'll come.

And this would also mean that if one buys the Premium Battle Pass once, then he's gonna get back all the V-Bucks that he spent and even more, (1500 per season) so that (if he doesn't spend them in another things) he will always be able to buy the Premium Battle Pass at the beginning of every season, forever. Or at least, if what I know is true.

Am I saying right things or am I wrong?

Yes, with the Premium Battle Pass you will earn enough V-Bucks to get the next season Premium Battle Pass with those earned V-Bucks.

And yes you will win all the previous levels rewards of Premium Battle Pass, but only for this season.