Peaks does not require you to give them your key. It is only stored in local storage and transactions are signed locally.

This is true with peaklock (which I only use for mobile) and keychain which is the most popular Hive solution for authentication. Your key is never sent over the wire in either scenario.

Hive also has multiple keys that compartmentalizes authorization, in most cases you only ever need your posting key which has no access to funds or critical operations.