Select Audit and specify the following under New Search
Date range for which auditing entries should be searched
Under Record types select Public Folder
Provide a meaningful search name and click on Search
The search will get queued, and should complete in a few minutes.
You can view the search results in the in the Purview Compliance portal and export the results as well.
Here are some examples:
Public folder deletion from client:
Public folder deletion from Exchange admin center or Exchange Online PowerShell:
The Microsoft Purview Auditing feature is enabled by default for all the tenants with the appropriate subscription and the auditing logs are retained for 90 days for Audit (Standard). They can be retained for longer periods with other subscriptions. Please check this page for more details on Microsoft Purview auditing.