To make it concrete, if there are two people in the economy: Alice and Bob. The only products that are exchanged is clothes and shoes. Every year, Alice sells 100 Galleons of shoes to Bob and Bob sells 100 Galleons of clothes to Alice. So the GDP of their economy is 200 Galleons. But assuming that shoes and clothes don't decay in one year, Alice and Bob will become wealthier and wealthier in apparel every year.

Perhaps surprisingly, neither capital stock nor asset price inflation is counted.

If your GDP is $100 billion and your growth rate is 0%, then next year your GDP will be $100 billion. This is normally considered to be "economy is the same size", not "added to the economy".

GDP is nothing to do with wealth and entirely to do with income.

Do you know if your assumption is true? GDP ignores depreciation/destruction.