Hello danielgauthier,
Welcome to the Apple Support Communities. I see you have a question about the App Store.
To double-check, when you tap App Store > Updates, does it say "Pending" at the top and still show the "Update all" button? Or are you only seeing your apps there listed as "Recently Updated?"
If you're still seeing "Update All," it sounds like the app updates may need to be installed. If that's the case, first try to Restart your iPhone, iPad, or iPod touch, and then tap "Update All" again. If this doesn't help, make sure you try updating on both a cellular connection, and Wi-Fi. To switch between these, you can swipe up to the bring up your Control Center and tap the Wi-Fi icon to disable it and try cellular data. Another step you can try is signing out of the App Store by tapping Settings > [your name at the top] > iTunes & App Store. Then, tap the Apple ID at the top, tap Sign Out, and then sign back in. Keep in mind that if you're an Apple Music subscriber, any offline content will be deleted and needs to be re-downloaded.
On the other hand, if you see only "Recently Updated," tap Settings > Notifications > App Store, and turn Badges off and then back on. If the red badge alert is still there, I recommend trying the restart and sign-out steps I posted above, as these might help here.
I hope this helps you.
Have a great day.