Where are signatures stored in segwit, and why are addresses different?

[Bitcoin]

Where are signatures stored in segwit, and why are addresses different?

So I'm researching SegWit, and as far as I'm aware, it re-organizes the data structure of transactions so that the ECDSA signature is not included in the preimage of the Tx Hash.

I am also aware that it doesn't even store the ECDSA on the blockchain. But where is it even stored then and how do nodes check for the signature when validating transactions?

Additionally, why does SegWit incorporate new address formats? I can't seem to understand how this would relate to changing the Tx Structure by moving the EDCSA's somewhere else.

All answers appreciated.

Source: Where are signatures stored in segwit, and why are addresses different?