Yes, if they pick and choose what gets a VAT and what doesn't, that will alter the cost structure. So there is that.

But it won't be because everyone is making more money so sellers can automatically jack prices up. It will be based on supply and demand (as always).

There's nothing automatic about it. It's more money chasing relatively the same goods.

Demand for essential goods isn't going to suddenly spike because people have more money.

Of course it will. It's the reverse of the substitution effect that is used in inflation discounting calculations. Times get tough? You switch from steak to hamburger. Got an extra 1000 USD inyour pocket? Back to steak.

Same goes for housing, energy, and all the rest.