Had the same experience you did. Changed my Pixel 2’s battery. Went smoothly. It works like new now. It took longer than expected, because I was extra careful. The tools were very useful and the adhesive sheet was a drop-in, I agree.
Once you remove the battery, you may notice parallel lines of adhesives on both sides of the surface, where the battery was. No need to scrape away these lines. They should be still sticky and usable. Removing these would be a hassle. Just add a strip or two of the double sided adhesives in the middle where the battery was, before putting in your new battery.
Besides the adhesive at the edges, there are 2 rectangular shaped adhesive patches at the top (around the speaker) and bottom (around the microphone). These are pretty thick, but can be easily chipped away with the pick. You start to see these as you gently lift the screen upwards with the suction cup and peer inside (use a flashlight). I did not need to use a heat gun or blow dryer. Just the pick and some isopropyl alcohol.