Multiple TypeScript discriminations based on different properties

I'm trying to build a complex REACT component which supports different use-cases. In order to simplify its use, I want to implement TypeScript discriminations types to better infer the props.

It's not useful to post the full example, but I can show you a simpler one, which is the following one:

interface ICategoryDiscriminationGame {
    category: 'game';
    gameType: 'AAA' | 'AA' | 'A';
}

interface ICategoryDiscriminationProgram {
    category: 'program';
    programType: 'software' | 'freeware';
}

type TCategoryDiscrimination = (ICategoryDiscriminationGame | ICategoryDiscriminationProgram);


interface ISaleDiscriminationPresale {
    saleType: 'pre-sale',
    preSaleCost: number;
}

interface ISaleDiscriminationRetailSale {
    saleType: 'retail',
    retailSaleCost: number;
}

type TSaleDiscrimination = (ISaleDiscriminationPresale | ISaleDiscriminationRetailSale);


type TExampleCompProps = TCategoryDiscrimination & TSaleDiscrimination;

export const ExampleComp = (props: TExampleCompProps) => {
    if (props.category === 'game') { // In here, intellisense infer only use 'props.category' and 'props.saleType' -> NICE
        console.log(props.gameType); // In here, intellisense infer also 'props.gameType' -> NICE
    }

    if (props.saleType === 'pre-sale') { // In here, intellisense infer only use 'props.category' and 'props.saleType' -> NICE
        console.log(props.preSaleCost); // In here, intellisense infer also 'props.preSaleCost' -> NICE
    }

    if (props.category === 'game' && props.saleType === 'retail') { // In here, intellisense infer only use 'props.category' and 'props.saleType' -> NICE
        console.log(props.retailSaleCost); // In here, intellisense infer also 'props.retailSaleCost' and 'props.gameType' -> NICE
        console.log(props.gameType); // In here, intellisense infer also 'props.retailSaleCost' and 'props.gameType' -> NICE
    }

    return <p>In example comp</p>
}

As you can see, inside the ExampleComp, the intellisense is brilliant, and works great. The problem is when I try to use the ExampleComp.
What I would expect is that, when I write <ExampleComp, the intellisense allows me only the props category and saleType, since the other ones cannot exist without first defining those two. BUT, instead, it just suggests everything:

So, the question here is: what am I missing that does not make the intellisense works correctly ALSO in the props?

TS Playground link