Is it intentional to have 'context' as first-level keys in JSON export file?
What's the reason for that?

It looks a bit strange to me. I thought that 'context' is a form of a description of the term to make it easier to understand the phrases when translating.
Why would I need context in the exported file apart from as comments?

Here is an example of what I get:

"Sent by the server when the invitation is accepted": {
    "notification.message_to_inviter_title": "...",
    "notification.message_to_inviter_text": "..."
}