Hi, alvinfromhomestead.
I see that you're trying to redownload applications you've purchased in the App Store after your iPhone 6s was restored. The issue is, they aren't downloading. Good job in restarting your iPhone to get it working as expected, and I'm happy to help.
Turn on Automatic Downloads for iTunes Store, App Store, and iBooks Store purchases -- If you're using cellular data to download the applications all at once, try downloading them one at a time. Tap Settings > [your name] > iTunes & App Store to see if you have "Use Cellular Data" turned on.
You can turn Automatic Downloads on or off over your cellular network on an iPhone or iPad Wi-Fi + Cellular. Go to Settings > [your name] > iTunes & App Store and turn Use Cellular Data on or off. Cellular Data downloads are limited to a file size of 150 MB or smaller.
If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network -- If you're using Wi-Fi, your iPhone may show that it's connected, but there may be other issues. You can also try downloading the applications while connected to a different Wi-Fi network.
Let me know how that goes.
Take care!