TRACKING: Migrate internal code to use Direct Message terminology #1344
Description
This is a follow-up to the user-visible #1288, as fixed by #1322.
- Rename/clarify internal variables; we could dedicate a specific task to this, but it may be more effective to migrate as-needed, where one part of the code is changed at a time, which relates to a particular other change underway
- Update to follow API changes; these will likely not be rapid, and support the older API for some time in any case