The Technical Engagement team would like to use the current https://twitter.com/wikimediatech twitter handle for promotion of Wikimedia technical projects on Twitter. This is related to the FY2019/2020 Q2 goal of "Create a blog by and for technical audiences where members of the technical community can post about their technical work" which apparently does not currently have a related Phabricator task.
I have researched this on the Twitter side and it appears to be a very straight forward process. The handle/username of an existing account can be changed and followers/following data will follow to the new handle. The URL to the tweet history does change when the handle changes, but because we are effectively usurping the current name for a different purpose we will be able to use either or both of the profile details and a pinned tweet at the legacy account name to tell folks how to find the new handle's feed.