Updating the `public` identifier for models to `leaderboard_public`

Currently, each model has an attribute `public` that specifies whether model scores will be displayed publicly through the BrainScore leaderboard. We want to add a new attribute specifying whether a submitted model's codebase is public. To avoid confusion between the two attributes, the current `public` attribute in the database, submission JSON files on Braintree, and website need to be updated to `leaderboard_public`.

The new attribute specifying whether a submitted model's codebase is public could therefore be called `code_public`.

Trace the current `public` attribute through the database, submission JSON files on Braintree, and the website. Identify every place that reads or writes the identifier, then verify that leaderboard visibility uses `leaderboard_public` and codebase visibility uses the new `code_public` attribute across those surfaces.

Written by the indexing model from the issue text.