Where are recordings stored before export?
In your browser's own storage, on your computer, written as the recording runs. They stay there until you open them in the editor, export them, or discard them.
A recording is streamed into the browser's storage in small pieces while it runs. That is what makes recovery possible if something interrupts it, and it is why free disk space is the real length limit.
Lifecycle
While recording
Pieces are written continuously. Closing the recorder tab or the browser leaves them in place.
After stopping
The recording waits for you to open it in the editor or discard it. Reopening the popup shows the pending recording.
After import or discard
Once the editor confirms it has the whole recording, or you discard it, the pieces are deleted from storage.
Clearing it manually
Removing the extension removes everything it stored. Clearing site data for the browser does the same. Neither touches files you already downloaded.