Or storing the key in localstorage?

To enable end-to-end encryption, you need more than local storage, you need local computation using local execution of signed and reproducible code. Javascript in browsers is fundamentally not such a platform, mobile applications are - to the degree you trust Google, Apple etc.

i guess by "each time" i was being somewhat ambiguous. it could mean each login, or each install, or each time the session clears.