I use GMail. A common workflow is to “Archive” an email when you finish reading it. This removes it from the inbox, but does not delete it.
When doing this on Gmail’s web interface, I am returned to the “Inbox” view. This means the next email is not opened and not marked as Read. This is a good thing, because archiving one message is not an any way related to the adjacent message in the Inbox. I don’t want to read that message, and don’t want to be forced to manually mark it as unread.
emClient does not appear to support the same workflow. I press “Enter” to open a message in a new window, press “A” to archive it, and the window immediately opens the subsequent message in my Inbox.
“Close original message window after deleting the message” does not support archiving, only deleting. I do not want to delete, I want to archive. This is a common GMail workflow.

Related request from 4 years ago: Setting to stop auto-view next email - Mail - eM Client
This might help you
Try setting “Don’t select first message” via Menu / Settings / Mail / Read / Message List” and uncheck Select first message in the list
That doesn’t work. The exact behavior I described still occurs after unchecking that option. You can confirm this yourself: double-check an email to open it, press “A” to archive, observe that the popup window is now displaying the subsequent email in the list. Contrast this with Gmail’s own behavior: pressing E to archive returns my view to the inbox list and does not display the subsequent email.
Gmail’s UI does a good job of phrasing exactly how this works in the settings:
Auto-advance
Show the next conversation instead of your inbox after you delete, archive or mute a conversation.
This is subtly different than emClient’s option which only talks about deleting the message, not archiving or muting. All of these actions cause the message to be dismissed, so the question becomes: automatically show another message, or not? It’s unfortunate that emClient’s option only talks about deleting, when it seems more intuitive for it to apply consistently to all actions which dismiss the currently-viewed message.