Welcome to the Apple Support Communities. I understand you're concerned about apps not restoring from a back up. Typically, when apps seem like they're stuck downloading after a restore, it's usually because the network connection was interrupted before the restore could complete. There are a few things we can try: If you can’t download or update apps, or if apps get stuck - Apple Support
First, tap on an app and look to see if it says that it's paused. If so, try pausing all but one app, then wait a little while to see if that one will download properly.
If that doesn't work, restart your iPhone traditionally and see if that changes anything: Restart your iPhone, iPad, or iPod touch - Apple Support
If there's no change after you restart the device, we'll need to try restoring from that back up again, but this time, make sure the device stays connected to the same Wi-Fi network throughout the entire process, and that the network doesn't get reset or disabled. Here's some information about restoring from a back up, just in case: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support
Be mindful that restoring from a back up can take a while, especially depending on the amount of information you're restoring, so it might need some time before everything is back on your iPhone as it should be. That should take care of it for you, but be sure to keep me posted so I can keep working on this with you if need be.