What's possible and how will depend I think on how your mail provider(s) have set up their systems.
Some providers, if they allow POP3 access, only allow you to access the INBOX folder of your mail account; indeed, if you have a system like that it, you may be unaware of any other folders. /Maybe/ there's ways to use POP3 to access other folders.
[Long ago I used a Demon POP3 account where in essence one owned a subdomain of demon so when one registered as eg "myname" ie myname.demon.co.uk one could use any address
xx@myname.demon... or
pqr@myname.demon... etc. (This was long before spam became a problem.) Normally if one logged into one's account one would see all the waiting mail but it was also possible to login and only see a subset, eg all the new mail that had arrived for pqr@... That mechanism probably doesn't exist anywhere these days but maybe some providers have a similar method of accessing a non-INBOX folder.]
Mail that arrives at a mail-hoster is probably placed in the INBOX by default. But if you are using a provider who allows filter rules to be defined on their server, you may be able to put mails elsewhere and/or set/unset IMAP flags on them. For example, if you filtered spam, on the server, to somewhere other than the INBOX then a POP3 session scanning the INBOX would never see it. If the place you put the spam in was visible to your IMAP sessions then you'd be able to review the results of the filter, in case stuff got filtered incorrectly.
Email client programs (on any of your devices) may also be able to interact with either temporary copies of the mails (grabbing them from the server as needed) or permanent copies (when they no longer exist on the server).
There are IMAP utility programs whose purpose is to grab mails from an IMAP server, to back them up. Possibly using one of those instead of POP3 for making backups would help you. See eg: Mailstore Home at
https://www.mailstore.com/ (which I have never used, just noted its existence). Or see eg
https://imapsync.lamiral.info/ for another tool (also never used by me). If you can write programs, you could also perhaps grab stuff with "curl".
I think you need to be clear what you're intending to do. What I think you maybe want is to make sure that every mail (of maybe just every non-spam mail, but that risks genuine mail being misclassified) is backed up securely in several places. Separately, you want to be able to see all the mails from umpteen places. I doubt it's easy to be able to see an on-server mail from umpteen places AND know it's been read from one person's iPad but not from someone-else's laptop, unless you (say) move every mail that one user has read to a folder that's for "read-by-me-but-not-you" and ignore the IMAP read flag. Maybe filters could copy mails so eg there's two copies, one for you to read and one for your wife ... but it'd likely get complicated quickly.
If you really do want to be able to see who read which mail when, you possibly need something other than an email client - some sort of database - to store emails in, with it logging who read what and when. I'd guess that software to do that would exist, in the corporate world, but I don't know of any.
One way to make security copies of mails is to intercept the email transport process so that when someone sends you a mail instead of it just being delivered to one mail-host, it also gets sent elsewhere. I think that requires your email address to be within your own domain (ie not something like a gmail address). Or, you could perhaps have a rule on your mail host's server that sends a copy of every incoming email to another provider (assuming your mail host allows that) so there's always (technical problems aside) more than one copy of every mail.