The mailbox doesn't automatically up to date

[tlle14]

Precondition

Refer: linagora/james-project#4329 (comment)

Actual Result

1. When there has a change (having a new message or remove a message), the mailbox doesn't automatically update.
   

2. When the User click the refresh button on the mailbox, it doesn't work.
   Let's refer the feedback from User

I had my test user connected for a week... when I hit the sync button in the mailbox, I noticed that op does a request getMessagesList to James with the after param to a week ago...which seems to correspond to when I logged in. Did a few more requests, still the same after param.
Then I logout/login, redo it and then after is set to today, to when I relogged in.

it's well... very inefficient. I would expect when you hit the resync button it actually fetch messages form the last sync and then would update that sync to the present moment. Or when I switch mailbox, as op does a full getMessagesList anyway. If you are logged in for a month, doing the sync from a month ago while I maybe refreshed my mailbox like 10 minutes ago seems not efficient

Expected Result

The mailbox should automatically sync when there has a change.

Environment

DEV platform