When all my apps are restored to a new phone, I still need to sign back in to most of them. It's a pretty understandable security measure, but it's a real pain with all the different passwords I have for the 40 apps I usually have installed on any given phone.
I found that the best way to easily sign back into my apps on a new phone is to use a password manager. I personally use LastPass.
LastPass will always be the first app I ever open on a new phone. Once I've signed into LastPass, I enable the settings that allow LastPass to automatically fill the usernames and passwords on apps that need me to sign in.
After setting up LastPass, I long-press the username field on an app I open for the first time and tap "Autofill." A little pop-up appears with the app's name and my username, and I select the relevant app.
LastPass does a great job at recognizing which app you're trying to sign in to. An instant later, my usernames and passwords are automatically filled in. It's much easier than tapping away several different passwords.
Effectively, LastPass is the only app that I type out my own username and password. All the other apps are signed in with the help of LastPass. The same would go for other password manager services, too.