For everyone who is experiencing this problem—yes, it does seem you got a bad battery.

I had this happen to me too, wrote iFixit and they sent a new battery that works perfectly. Honestly, this is almost a reason to do the whole thing without detaching the screen first. You can keep the screen bent less than 90° that way and as long as your old battery pops free easily, it allows for testing with the phone partially open to make sure it can run 10-15 minutes before buttoning it all back up, which is how I did it the 5th time I tore my phone apart to install the second replacement battery lol.