iPhone backups

I just got a new iPhone (SE 2020) to replace my difficult to charge older SE (Charger plug in the old phone is worn out) . I backed up everything to my computer and the cloud before installing all of that on my new phone. However, when I downloaded the backup to my new phone, it looked nothing like my old phone and many of apps I had purchased were missing. Wasn't happy. I erased the new phone and discovered if you put the old phone and new phone next to each other the data and apps will move over to the new phone. This worked perfectly. Very happy, except for one thing. Suppose I had lost my phone and needed to use the backups on the cloud. Am I wrong or would I have to reinstall most of my apps? I must be missing something. Thanks