Thread-like email management

Question

I will quote exactly the initial paragraph of another question, because it explains the issue perfectly:

A features that I liked in GMail was that when an email arrived that was a reply to an earlier email, Gmail would display all of the previous emails along with the new one in a single thread in my inbox. Importantly, GMail would display emails in the thread even if they had been previously archived.

The OP of that question wants to have a similar functionality in Thunderbird. My question differs in that I would like to reproduce this kind of functionality without being bound with a specific client. I have access to an email account via IMAP, and I actually access this account through a client on my laptop, through an email application on my smartphone and through the web interface when on a public computer.

To be more specific, I would like to see the entire conversation to be visible in the inbox whenever an email arrives. The entire conversation should include the other emails I received (as To: or CC:) and the ones I sent. This should happen even if I archived the conversation earlier (by archived I mean moved it to a folder other than the inbox).

This looks like a basic feature to me. Gmail has offered it for about a decade already. Yet, from the little techincal knowledge of email I have, I know this is not how email works. And I would find difficult to migrate away from Gmail specifically for this reason. So, the question is: Am I missing something, or having this reasonable way of managing conversation really difficult with standard email providers?

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(A non-solution)

The only solution I can think of that does not require clients to actively perform this kind of operations when checking the email is to have a script running on a server, checking the email every, say, 5 minutes, and move the conversation from the archive into the inbox when a new related message arrives.

While I have the skills to do that and I could run the script on my always-on Raspberry Pi, I have several problems with this solution:

• It relies on my server's uptime
• If I happen to check the email on my laptop after a message as arrived but before the server has moved the conversation I will not have the desired result in my inbox (i.e., the entire conversation won't be there)
• I would have the feeling of reinventing the wheel, because I think this is a very generic problem and I can't believe a better solution doesn't exist.