Up to you whether you want to tell the seller know that you will file a claim. I would not, due to you have given the seller time to resolve the issue.
To be clear, you won’t receive your refund right away when you file a claim. As I stated earlier, PayPal will give the seller time to respond and they may ask you for further follow up questions possibly. PayPal will make the ruling based on responses from both buyer and seller. The whole process will take up to a few weeks depending on how soon each party responds. Once you file a claim with PayPal, you will live with its decision and it is considered final.