Just finished replacing the antenna and the battery on Surface Pro4. I highly recommend ignoring the steps to remove the battery without removing the motherboard (mb). Removing the mb is less difficult than trying to get the battery ribbon in and out. As many have learned, you can brick your mb, and, like me not get it aligned properly causing “no battery detected”. After removing the mb, I was able to realign the battery ribbon properly and all worked great. This video is great at removing the mb. Don’t worry about removing the buttons, left speaker, or SSD (they won’t interfere).
Youtube video number: n74Pc_luSGI (How to Take Apart the Microsoft Surface Pro 4)
Once mb is removed, remove the battery, and install the new battery, insuring the battery ribbon is on the plastic locator pin (not in instructions), place adhesive under ribbon to hold in proper place for contacts on the mb.
I purchased these and both work great:
Battery (Amazon ASIN): B08595GYBN
Antenna (Amazon ASIN): B08PV8SZ3R