Releasing Addon to coincide with Murkmire release
 

This is the first time that my addon is ready to go for Murkmire. As such, I am unfamiliar with how Bethesda releases their ESO DLCs. Do they launch at midnight or later in the day?

Thanks! (and humble apologies for the noob question)

The will update on the pre-informed (check the official ESO forums for the timeframe) server maintenance timeframe.
Servers will be unavailable during this time and afterwards pretty the same as the PTS source (+ some fixes etc.) will be on live as well.

As users are able to login again tzhe API version raised and everything should behave liek on the PTS before.

Servers usually go down at 4 am EST on the night before the patch. The time that they come up after that varies, but probably not until noon on the next day. You can also do a multi patch supporting version which supports both the old and new version of the game. Depending on how many changes there are, it may or may not be feasible. You can use GetAPIVersion within the addon to block out new (or old) code.
Since it's so close to the patch, you're probably best off just pushing it when servers go down or tomorrow morning. Or you could just push it now. Patch is close enough that it probably won't matter much.

Through trial and error, and also reviewing other addons, I learned I can stack API versions:

The addon will now be seen as current in 4.1 and 4.2.

You can also use the placeholder $(APIVersion) in the manifest tx file to load different filenames for the different APIversions (live, pts).
Example:

This will load the file source_100024.lua on live and source_100025.lua on PTS.
Be sure to always load a "fallback" version before so if the API changes one day and your addon is missing the file, your addon won't break!