Why my iPhone battery health drops so fast 4 months and now 87%?

That iPhone model, discontinued by Apple, most likely was manufactured in September 2019, and its battery might be even older.

For your peace of mind, you can make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.

Bearing in mind that that value is approximate and is related to when that battery was new, what iPhone model are you using?

Regards

Giulio