At the end of the news program Tagesschau the host always says "Ich wünsche Ihnen noch einen schönen Abend". Today a German typed that to me as well at the end of a conversation. I understand the sentence, but what's the functionality of "noch" here exactly? Is it here to signify a kind of meaning of "in addition", "before we go", "one last thing"?
To me, noch refers to the fact that the evening has already begun. An approximate equivalent in English would be:
Enjoy the rest of your evening.
You can also say on Sunday after shopping at the baker's:
Ich wünsche Ihnen noch einen schönen Sonntag.
But you wouldn't say it on Saturday – then you'd need to omit the noch.
Re. comments: Sorry for being ambiguous above. I meant that on Saturday, you wouldn’t wish noch einen schönen Sonntag. You can obviously say noch einen schönen Samstag. Or, if there is reason to explicitly refer to the next day (e.g. because you have been told that some special activities will be taking place): einen schönen/erträglichen/etc. Sonntag (dann) (without noch, and with an optional dann that emphasises that you are referring back to your previous discussion about the next day’s activities).
This is one of those German particles that are tricky to translate to English...
I would probably go with
I wish you a continued pleasant evening (after I stopped talking to you).
As @EndreBoth mentions in his answer, this implies, that said evening has already started. And as you mentioned, it also has a bit of "goodbye" in the background.
In French, I'd translate it to "Bon soirée!" instead of "Bon soir.", if this is any help.