Hello GabrielVM,
Thanks for asking your question here in the Apple Support Communities. I understand how important it is to have the ability to update your apps from the App Store. Here are a few things you can try to get this working again.
The first thing we want to ensure is that all your data is safe. You can make a backup in iCloud or iTunes. Use this article for help with that: How to back up your iPhone, iPad, and iPod touch.
Then, I want to recommend you try turning the iPhone off, then back on again. Sometimes, that is all that is necessary to get all the connections reset, and everything working properly again. This help article from Apple will assist you to do that: Restart your iPhone, iPad, or iPod touch.
If you still have issues, try going to Settings > Wi-Fi and disabling Wi-Fi. Then, go back to the App Store, and see if you can do the update. If this works, it means there is some port closed on your home network that will not allow some part of the process involved in verifying your Apple ID and payment info from the App Store to finish. Some things that can block this are third party virus protection, firewalls, or proxies that hide your identity from the internet. These do not have to be set up on your home computer or iPhone, as they can be set up directly on your router. Some security apps also do this, but are only called Security or VPN. There are literally hundreds of such apps you could install on your home computer, router, or iPhone that block incoming ports which will not allow this feature to work.
If you still have issues, do this reset: If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network. Use the section titled 'Still can't connect?' and follow the steps to Reset Network Settings. This brings network settings back to the factory defaults. You can try the updates again using cellular only, or turn Wi-Fi back on again, and connect to your home network by entering in the password for it. Then, you can try updates again.
If you are still experiencing issues with the updates or making a purchase, you will need to contact AppleCare and have them check your account. There may be a block or some sort of protection on your account that they can help you bypass once they verify you are the owner of the account. Use this link to contact iTunes. Contact Apple Support. Select the second option "Purchases, Billing & Redemption".
Thanks again for checking out the Apple Support Communities. Have a great rest of your day.