Following Step 3 in reverse order, you can first screw everything but the plastic cover back in place

Then, you can put in the new battery. You might want to glue it in a little (e.g. using the rest of the glue that you removed previously), but keep in mind that you will need to remove it again the next time you change the battery.

Gently snap in the battery connector

Screw the plastic cover back on

Gently press the Display back on and heat it up again. This made the display stick again reasonably well for me

Remember to fully charge your new battery before trying it out :)