I recently purchased a new iPhone 13. I took my iPhone 11 to have everything transferred

I took my iPhone 11 to have everything transferred I have not backed up the iPhone 11 and a very long time because of storage issues. He told me that I needed to back everything up and then continue transferring everything as I have was already trying to do. Started the back up last night it shut the phone down throughout most of the night. I’ll get flashes of my home screen and then it all switch back to a circling icon in the center of the phone. Do you believe it is still backing up? I’m fearful to lose the photos of my kids