The only thing you said that is true is in the last sentence. The basket of goods affecting inflation is heavily influenced by the cost of housing. All you care about when holding a store of value is how much of that denominated fungible asset can be exchanged for things you need to live.
Ah, so according to you my first sentence is false then? Let's see what a simple Google search yields:
>Inflation is the decrease in the purchasing power of a currency.
>Inflation is the decline of purchasing power of a given currency over time.
>Inflation is a persistent rise in the average level of prices over time in a given currency.
> Inflation occurs when prices rise, decreasing the purchasing power of your dollars.
Those are literally the top search results for "inflation" when I Google the term. Now certainly your Google search for that term may differ from mine and you are certainly welcome to share your findings. Until then I will rest satisfied that my first sentence expressing that inflation is almost always understood to be with respect to a currency is also true.