I have followed step by step the process for adding an entitlement to a product in playground and it is not showing up in classic.

Hi @Vibha Tripathi ,

If you are not able to see the entitlement option even in classic version, try adding Entitlement Templates from related list section to the page layout of products. For this search for products from quick find and select page layout and then select edit next to product layout and add "Entitlement Templates". 

https://trailhead.salesforce.com/trailblazer-community/feed/0D54V00007T4QOxSAN

I just found the strange part that the new entitltement template created directly under Entitlement tab does not really exist. I need to create the template from Setup/Entitlement template.

https://trailhead.salesforce.com/trailblazer-community/feed/0D54V00007T4Nj7SAF