I wouldn’t do the cut too early. Try to ease both white tapes out without breaking them an inch or so if possible. Its not easy getting the angle of pull right as you end up with very close quarters with some semisharp parts.
Reattaching the digitalizer connector is a ##&&% if you ty to keep the innards 90 degrees to the case using a rubber band and a box/can. Hold the innards in your hand to line up this connector. Once that is done the other two connections can be done with stabilized innards banded to a box/can.
My phone did not have this bracket. Our other SE did.
This is a lot easier if you take advantage of the fact that the coefficient of expansion is different between the metal case and the innards. On my second battery replacement, I heated a wet washcloth in the microwave, put it in a plastic bag, and laid the phone on it. Voila! Cracked the phone open almost like opening a refrigerator door!
Having two SE’s needing batteries, I ordered an extra battery. The extra battery did not come with the Phillips replacement screws. It would be helpful if every battery came with a set of case replacement screws.