The majority of what you are talking about (read / unread, user tags and other such things) is handled by the IMAP server. eg; I routinely start drafts on mobile, save it, then continue to draft on a computer before sending. Also set flags on mobile for follow up later on desktop. Almost none of this depends on the client itself, it's all stored in IMAP.
Late addition but yes of course the apps must support those IMAP features. They work hand in hand for this functionality.
Presently if you aren't able to do any of the above something is not configured correctly. Some apps have differing opinions on where the sent/drafts/deleted folders should be for example.
