Inbox is an automated mechanism that sorts replies by different categories. It helps you quickly find contacts who are interested in your offer and reply to them manually. You can reply to their email via the Inbox tab, however, further responses to and from the prospect will not be reflected in the thread. This means that you cannot fully substitute your original email inbox with the Inbox tab on Reply.
These are the default categories in your Inbox (you can also add custom categories, but without setting keywords for them):
Do not contact
In addition, you can use the Unread filter above the category list to quickly access unread emails and mark selected threads as read/unread:
Other options to use inbox sorting results:
Reports tab. You can see the percentage from all replies in sequence as Interested.
Zapier. You can filter contacts by Interested using the New Email Replied trigger.
Integrations. Update contacts in your CRM using native integrations.