I successfully followed this guide to replace the battery in my Xperia Z5 Compact. The only problem I ran into was the old battery strip snapping when I tried pulling it out. I had to use a heat gun to soften up the old adhesive strip to remove the old battery. The parts list is missing adhesive for the replacement battery, so make sure you have a suitable way to affix the replacement battery to the board. Everything went back together smoothly, and the phone is fully functional. Being completely inexperienced with phone repair, it took me about 90 minutes to complete this guide.
As of Sep 2021, the battery adhesive strips are still not in the parts list. I also had to source my own battery adhesives in the middle of the repair.