Can I replace the screen and battery at the same time?

I've got an iPhone SE 2020 that needs a battery replacement. The screen isn't in a great condition, but will probably last a bit longer. Since both battery replacement and screen replacement look like bigger jobs, I'm wondering if I can do them at the same time?

It looks like the repair guide for the battery replacement suggests removing the screen - can I just swap the new one in at that step, or is there some extra steps? It looks like I'll need to do something with the home button too.

Has anyone done this, and is there a recommended order of steps combining the two guides?