In the case of offline recording the data is stored in indexedDB. Localstorage limits are typically too small to store a reasonably sized session recording.
How much data is stored on the user's disk per session?
The actual amount in bytes will vary with the complexity of the app, the amount of activity in the session and the length of history the recorder is configured to store.
Typically this will be a few MBs for the default 10 minutes of history.