Replace an iPhone 8 battery myself

Apple does not support that and do not sell parts for the iPhone 8. Sorry. The self repair is only for the iPhone 12 and above.

Save yourself the grief. Apple still does battery service on the iPhone 8. It's only US$69. The cost estimator here:

iPhone Repair and Service - Apple Support

show s the iPhone 8 and 8 Plus are boths till eltgle for Apple battery service.

If you have the experience to know how to avoid wrecking the screen when you try to take the phone apart.....and....you realize that you cannot find a genuine Apple battery to install.....and.....you also realize that the non-genuine battery will not display any settings regarding Battery Health.....and....you understand that Apple will not even touch the phone if you have any difficulties due to tampering by an unauthorized person.....and....you also understand the phone will have zero trade in value at Apple if you want to upgrade to a new phone.....have at it.

More information about self-service repair is here Self Service Repair - Apple Support

but as you are finding out, it does not include the iPhone 8.