[Feature Request] Verbose mode option for longer running operations

Currently, long-running operations such as sample posterior (mmm.sample_posterior()) and budget optimizing (budget_optimizer.optimize()) can take a significant amount of time. An option to have some visibility in the progress would be highly beneficial, especially in the testing phases to better adjust development expectations, parameters, and infrastructure that we run on.

Proposed solution: A parameter to turn on verbose mode with iteration progress or completion percentage checkpoint prints to provide regular updates for longer-running operations.

Start at the mmm.sample_posterior() and budget_optimizer.optimize() entry points and identify how their long-running work can report progress. Done means users can enable a verbose option and receive regular iteration or completion updates for both operations, with coverage for the new behavior.

Written by the indexing model from the issue text.