we cannot sync our data in a stable manner.

What is the imap server? mainstream provider?

1 - The timestamp of the email was not kept correct on the backup (mtime), so after the migration, all emails are being shown as if they were received/sent on the same day, this problem was mitigated using this script : https://github.com/mikebrady/imap_maildir_date_fixer (if it can help someone else).

Ok.
Imapsync can overcome this issue with the option --idatefromheader, it does this on the fly
https://imapsync.lamiral.info/README

     --syncinternaldates : Sets the internal dates on host2 as the same as host1.
                           Turned on by default. The internal date is the date
                           when a message arrives on a host (Unix mtime usually).
     --idatefromheader   : Sets the internal dates on host2 as the same as the
                           ones in "Date:" headers.

2 -The email flags were not recovered, so all emails are being shown as unread.
The source server is still accessible despite it's poor service, is there a way using imapsync to sync email flags from the source server after the local migration?

Imapsync resyncs flags by default.
If you want to add the \Seen flag to all messages:
https://imapsync.lamiral.info/FAQ.d/FAQ.Flags.txt
...

On Unix:
  imapsync ... --search1 UNSEEN --regexflag 's,,\\Seen ,'

On Winwows:
  imapsync.exe ... --search1 UNSEEN  --regexflag "s,,\\Seen ,"

Hi, and thanks

The source email server uses icewarp as a mail server.
From the backup data, we found that the metadata are included in several .data files, and it's not usable directly by dovecot.

From your response, I understand that it is possible to get the correct state of the email after being migrated from a backup just by executing a sync from the source server?

I will try it and report back

Regards.