Support for auto-filing sent emails

I am looking for a solution to this scenario in the New Outlook:

1. I send tens of emails per day
2. The sent emails are stored in the Sent Items folder
3. I need to manually move each of them into the sub-folders in my Archive folder - e.g. one for support cases

Is there any way to automate the step (3) - i.e. to automatically file the sent emails into the folders they belong to?

The Classic Outlook had "When replying to a message that is not in the Inbox, save the reply in the same folder" which is not present in the New Outlook.

Maybe the New Outlook should have something even more powerful? In addition to this feature, a button suggesting into which folder each message should be filed?

Finally, the Outlook Rules are very powerful but they do not apply to the sent emails. Maybe time to generalize these?