Re: Vegeta should not have gotten the win on Toppo because of lack of "chemistry", whatever that means these twenty minutes.
Vegeta spelled it out with that Final Explosion that Toppo had essentially gone the Majin Vegeta route in his GoD ascension - a desperate and cheap power-up once he became convinced that power was all that mattered, damn any other attachments. Had this been Z Vegeta, he would completely agree with Toppo. But this is Super: Vegeta has gone down this road before, and saw for himself that the gambit wasn't worth it, both morally, and empirically since Majin Buu survived his attack. He's got a family he wants to protect, a Saiyan comrade he wants to keep his promise to, and most of all, a Saiyan pride that he has learned to redirect and hone altruistically, and this has granted him power he could never have imagined as a Majin fighter.
Vegeta needed to be the one to beat Toppo. Toppo obstensively was a Vegeta with a very warped sense of black and white morality - remember that Toppo refused to associate with Universe 7 because he thought they were tainted by evil and he didn't want to be corrupted. Toppo was a warrior with pride in justice to spare, but when he eventually got over it, he went in the completely opposite direction. The best person to take him down is the one who has grown beyond this "Might is Right" phase, and in wholesome ways. Jiren even slags Toppo for this in the end, and praises Vegeta for never letting go of his pride through all his struggles in this tournament, so the message was clear.
The fight also proved that Vegeta wasn't just support backup for Goku in his tagteaming with Jiren, he can hold his own. He's proven that he has the power to defeat and surpass actual Gods of Destruction, literally obliterating Destruction energy that Freeza couldn't handle, which, now given that this is the endgame for Super, was needed to show he and Goku can overpower Beerus in a fight, albeit indirectly, since we're not getting this fight now. This final fight for Super is between mortals that can either stall out, or outright overpower GoDs - Jiren's not the only member of this club now.
Vegeta's proven just how far he's come as a fighter, and as a person, using the very attack he used to atone for his past sins and surviving, proving that the core of his character in Super is "A power that Toppo can't Destroy." Worthwhile episode.