A wallet does not contain tokens in the way a pocket contains cash. The tokens are entries in accounts maintained by the network. Your wallet protects the secret needed to authorise instructions that change those entries.
The key is the authority
A private key produces signatures that anyone can verify against its public key. The network does not need your name, device or permission from a company. A valid signature is the permission.
Seed phrases are human packaging
Most wallets encode their root secret as a list of words because words are easier to record than random bytes. Anyone who learns that phrase can usually recreate the same keys on another device. There is no recovery desk that can distinguish them from you.
Signing is the critical moment
A wallet prompt is not a login confirmation. It may authorise a transfer, grant another account control or interact with a program. Read the requested network, assets and permissions before approving anything, especially when a site creates urgency.