Where exactly is all our wallet info stored?

When we look at individual cryptos, the crypto itself is stored on the network/blockchain. Your private key is your ownership and access to the crypto which is stored with you, and it links to the public key stored on the network.

Makes sense. But how does this work with wallets and seeds?

How does a certain set of words allow me to pull up my multicoin wallet with several different cryptos?

Where is this information stored? How is it possible that I can use this same seed with another wallet provider and still pull up my wallet with my coins from multiple blockchains (as long as the coins are supported)?

What network is this information being stored on?

EDIT: I remember in the early days of crypto we would have to save the private key for every coin, but these days we just use wallets. It's probably safer and more convenient to stick with seeds, but is it possible to get the private key for each of my coins using my seed?