It does support server side tags on supported IMAP servers, which Dovecot is one of them, but the way it works was in question. IMAP servers don’t have a method where you can sync the tag listing management you see in the client. So when you create a new tag in the eM Client (or Thunderbird) interface, that is not sync’ed to the IMAP server. When you do tag an email with a client based tag you created, it sets a IMAP Keyword using the tag name you created in eM Client on the email itself and corresponding folder. If you create a new tag for example in Thunderbird and then tag an email, then eM Client will show that tag on the email, but that tag will not be listed in the eM Client list of tags, it will show only on the email itself.
GMail as you mentioned has a separate API to access GMail created labels, which eM Client supports. So when it comes to GMail, eM Client supports the API to allow you to manage the tags. When it comes to IMAP eM Client uses the “Local Tags” listing, and if the IMAP server is supported then when you set a local tag it will also set that tag on the email itself on the server side.
This is why server side storage of tags is limited in eM Client to specific IMAP servers. The only feature I can think of that could be added to eM Client would be an on-demand option to add the known server side tags used on emails to the tag manager “Local Tags” listing. Of course such an operation would require eM Client to scan all the emails to find out what has been used, and then add it to your “Local Tags” listing automatically. An issue with doing this is that if you delete a “Local Tag” it doesn’t mean it gets removed from the IMAP server, since once again IMAP doesn’t support a direct mechanism for removing IMAP Keywords from emails efficiently. So what ends up happening is you can remove the “Local Tag” from eM Client, and still have emails with that tag since it needs to be removed from the emails themselves. If you sync’ed the listing again then it would be re-added unless you remove that tag from all emails that had that tag in your mailbox. So that is why such a feature is probably not worth the effort.
That is why I say IMAP server support for tags is sort of a hack and is not a true tag management server sync type setup like what is supported for EWS and GMail since they have custom API’s for such functionality. GMail is weird since it doesn’t even support folders, it supports labels only. But when you use IMAP on GMail, the GMail IMAP server actually converts your labels into folders from an IMAP perspective, since IMAP doesn’t have any label/tag support built in. Label management in GMail comes by way of their API interface, not IMAP. In general GMail IMAP support is subpar.
Hopefully that makes better sense. Unfortunately IMAP is very old and missing some things like tags/labels, advanced push support, and 2FA. To support such things you have to use creative hacks which don’t always support everything newer protocols like EWS/MAPI does. When it comes to tags/labels it uses IMAP Keywords, for push support you have to use IMAP IDLE (which most mobile devices don’t support very well), and for 2FA you have to come up with creative password combinations. Not ideal, but it does provide some sort of server side support.