Sanji and Don Krieg are probably the most thematically connected strawhat/villain combo in the series. One of Sanji's core ideals, as much as, if not more so than not hitting women, is always feeding the hungry no matter what. This is obviously caused by his traumatic backstory with Zeff on the island. When Gin showed up, the other chefs told him not to feed him because he wasn't paying and he might come back with more pirates. Sanji fed him anyways and sure enough, he brought Don Krieg. They even tried to attack Sanji to prevent him from feeding Don Krieg, but his ideals wouldn't allow him to let him starve. And when Don Krieg attacked, just like the chefs said he would, Sanji's ideals were thrown into question because the resteraunt he had dedicated his life to protecting out of debt to Zeff was about to be taken. A lot more was on the line for Sanji than Baratie. If Krieg won, it would have been Sanji's fault because of his ideals. He would have had to abandoned his core beliefs, and probably ended up as a completely broken man. The whole thing was fundementally Sanji's fault, and it was a battle for the validity of his values. I'd say that's a pretty damn strong connection.
No not really all you said right now is compeltly interchangable with any other villain, circusntances made Don Krieg starve and made that arc about stavation on purpose.
Thematically Don Krieg has nothing to do with hunger or stavation, he's a captain of a large fleet. he's a piece of shit, he's literally called Foul-play Krieg, he's deceptive and cunning, uses cheap tricks and weapons and relies on his armor, that's the character's themes. If he was known to starve his subordinates ocasionally as a form of punishment sure, but that still doesn't change the fact, Sanji has no connection to Don Krieg like i said, he just happen to appear in the Baratie, there's no history.
You're confusing the arc themes with character themes. Wano has themes of identity, doesn't mean Kaido has that theme.
I don't understand why Carrot fans always use this to try and justify Carrot not fitting the mold that every last strawhat fits. Sanji isn't even the weakest link in that pattern. Jinbei is since he didn't need Luffy's help at all. He was more than capable of beating all the new fishman pirates by himself.
The only "mold" every SH fits is the role/dream. Everythign else is guesswork