The glue as of the 12 series is incredibly strong. I'm definitely not new to the game and working only with a suction cup, I damaged the screen too, because I couldn't lift it far enough. Therefore, I too had to buy a new screen. 130€ poorer, I would opt for borrowing the display removal kit Apple sells at selfservicerepairs.com. It's around 50 or 60 Euros and worth it.

Bought the replacement battery from iFixit but upon reassembly, the 13 mm tri-point screw (the right one) took like 15 minutes to get it properly alined. With the original battery, it was first try, as was the left 5,6 mm. Keep an eye out for that!