That's not really what the app does, nor would you want it to be able to since it would be a bit of a security risk. Your best protection against data loss will always be good backups. Still, I'll give you some info to send you down the appropriate "rabbit hole". 🤓👍 (No promises though...)
Most of your settings should sync when you connect the new phone to your Google account. Not all of them, but apps and such will. As for your home screen, you will likely have to rearrange that yourself. Have a look at this link from Google, it will give you instructions on restoring the stuff that is connected to your Google account. Even if you didn't explicitly enable the backup functions in the phone settings, you can still get your apps back from the Play Store.
Back up or restore data on your Android device
Hopefully you enabled the backup settings in the phone, but if you didn't and you're intent on having the whole thing restored there are forensic tools that can extract most, if not all, of the data. They may be able to (essentially) make an image of your old phone and mirror it to your new one. That would definitely accomplish what you want to do, but I have not used any of them in years. One caveat (discussed in the following article at length) is that you may not be able to access all of the data unless you enable(d) USB debugging. If you did not, then some software forensic tools can bypass it on some phone models, but it is difficult to guarantee anything. Have a look at this article about using a forensic tool:
How to use a forensic tool to extract data from a broken Android phone
Beyond that, your options are basically:
- Get the screen repaired, which may be a waste since the phone may not work properly anyway.
- Go to XDAand see if anyone there can help you. There are some pretty amazing people on there who can do incredible things, but there are limits to everything wizarding-related.
I know these aren't the answers you were looking for, but they are the answers that exist. 🤷♂️ Hope it helps.