Should I buy a new iPhone if the battery level is at 87%?

The acceptable Maximum Capacity is 80% or more. If it falls under 80%, you can simply replace the battery and there is no need for a new phone. The cost is $89(US) on the iPhone 13 Pro Max.

iPhone Battery Repair & Replacement - Apple Support

I am assuming that you are referring to the Battery Health of your iPhone at 87%. Apple recommends that the iPhone battery should be replaced once its battery health has reached to 80% or lower. This means that your Battery Health is fine and progressing normally. It is not time for a new iPhone. You know you can always just get the battery replaced when it reaches close to 80% for less than $90 and your iPhone will operate normally.

Axel F.

You won't need a new phone. Just have the battery replaced at the Apple Store or an authorized Apple service shop when the Maximum Capacity is down to 80%.

That will be 6-8 months or so from now.