naming of timestamps are unclear

I had a deep dive into the metadata the last days and noticed that the naming of timestamps is often unclear and the same name is used multiple times across the API. It might be helpful for a user to have a unique name for all values across the API. For example:

* created_at -> entry_created_at
* last_sync -> repository_last_sync
* pushed_at -> latest_push_to_repo_at

I would also expose the pushed_at value at the top level, as this is likely to be a very important value for most users, showing the last time the project had any active development activity.

The issue names no files, tests, or entry points. Start by locating the API metadata definitions and serialization code, then map every timestamp name and its consumers. Done means agreeing on unambiguous names across the API and exposing pushed_at at the top level without breaking existing users.

Written by the indexing model from the issue text.