Kopano-WebApp/DeskApp doesn’t offer calibri font, so if half your company uses Outlook and half uses Kopano DeskApp, you can’t have those DeskApp users write in the same html font (which was set as corporate standard by the outlook users).
Kopano-WebApp/DeskApp doesn’t allow embedding images, for which there is a workaround (previously setdefaultsignature.py, but this does not seem to exist anymore, now there is kopano-webapop_admin.py which should be used along with a manually created signature in a text editor with the image embedded as base64 code). This does actually work, and making it work and having the image properly embedded for two users only took me two hours.
to be able to send mails from the Kopano clients (WebApp, ActiveSync clients) nothing need to be changed in the configuration of kopano-spooler or the kopano_spooler container
if you want to change configuration in the mail container, then I suggest to check their docs (you already linked to https://docker-mailserver.github.io/docker-mailserver/edge/config/security/understanding-the-ports/) and ask in their project if you encounter any issues sending mail for example through Thunderbird. In my eyes this is out of the scope of the kopano-docker project, but should be possible to achieve through configuration nonetheless.
running a second instance of docker-mailserver is not necessary
PS: why did you delete your topic regarding the use of linuxserver.io swag?
the simple solution to this would be creating a calendar in the public for this and have either each employee or hr add appointments for the birthdays to it. I have been told however in the past that these kind of calendars are difficult from a data privacy point, laws may differ where you are.
You will not get reminders for it however, since this only works for calendars in your own store.