Apple doesn't make original parts available to third-party repair shops other than Authorized Apple Service Providers.
If you have the battery replaced with something other than an OEM part, you wouldn't be able to see your battery's maximum capacity in Settings>Battery>Battery Health. I believe there will also be a permanent notification in Settings that you have non-original part. But, most important of all, Apple may refuse to perform any subsequent service on your phone.
I highly recommend you get the work done by Apple:
Genius Bar Reservation and Apple Support Options - Apple