Are the results of freshness stored anywhere?

Yes!

The dbt source freshness command will output a pass/warning/error status for each table selected in the freshness snapshot.

Additionally, dbt will write the freshness results to a file in the target/ directory called sources.json by default. You can also override this destination, use the -o flag to the dbt source freshness command.

After enabling source freshness within a job, configure Artifacts in your Project Details page, which you can find by selectng your account name on the left side menu in dbt Cloud and clicking Account settings. You can see the current status for source freshness by clicking View Sources in the job page.