People in Photos

Using my 13" M1 MacBook Pro I've been culling a library of about 16,000 images down to around 8,000 and naming people as I go. Often, I can only see blank rectangles with names on the People page and get the following message at the bottom - Photos will finish updating your people when you're not using the app and your Mac is connected to power. Should I keep the app open in the background or close it? If Photos should remain open, will closing all other apps make this process any faster?