Desktop at the office, laptop for travel, Outlook on both. Keeping them matched by hand is failing badly. Read mail shows unread, replies exist on one machine only, folders drift apart.
POP account with a local PST, if that matters. What is the sane architecture here?
It matters completely: POP with a local PST is the whole problem. POP downloads mail to whichever machine asks first and the PST holding your mail knows nothing about its twin on the other machine. There is no sync layer to fix because the architecture never had one. The sane architecture puts the mailbox on a server and lets both machines read the same copy.
The fix is converting the account to IMAP or moving to a hosted Exchange style account. Same address, different protocol: check your provider's settings page for IMAP support, then add the account fresh as IMAP on both machines. Read state, replies, folders and deletions all live server side and both Outlooks mirror it. Upload your PST history into the IMAP account by dragging folders, or keep the PST attached alongside as a read only archive on one machine.
If the provider is IMAP hostile or the mailbox quota is tiny, the alternative is redirecting the address into an account that syncs properly, an Outlook.com mailbox for instance, either by forwarding or by moving the domain's mail hosting. More setup once, then the same everywhere behaviour forever.
The tempting shortcut to explicitly avoid: putting the PST inside OneDrive or Dropbox and opening it from both machines. Sync clients and open PST files corrupt each other with depressing reliability, every mail forum including this one carries the wreckage threads. Server side mailbox or nothing.
Provider supported IMAP all along, nobody ever mentioned it. Re-added on both machines, dragged the history up and watched a read message go grey on the laptop seconds after reading it on the desktop. Years of drift, over.