I have used K-9 Mail for quite a few years and the 5.8xx release has been a good one, bringing better, recent Android compatibility up to date and working very nicely, see K-9 Mail for all the details.
Prior to 5.8xx the e-mail time is when it landed in K9! (Turns out K-9 needs a "Date" header in the e-mail, without this it does as described) See Inbox sorted by time mail was fetched to phone and not received on server · Issue #2599 · k9mail/k-9
I cannot see server connections details to check they are secure for IMAP.
When a filter is applied, like "Unread" then I cannot swipe through the messages
However it does show the e-mail time as when it landed in my account on the server.