The short version: App updates live under your App Store profile icon, not in a bottom Updates tab. You can also turn on automatic updates in Settings.
Apple moved app updates out of a dedicated App Store tab when Arcade arrived. The path still confuses people who learned the old layout. Here is how to update apps on a current iPhone.
Update apps manually
1. Open the App Store.
2. Tap your profile picture or initials in the top right.
3. Scroll to see pending updates. Tap Update next to one app, or Update All.
4. Stay on Wi-Fi for large updates when you can. Cellular downloads may be limited by your Settings.
Turn on automatic updates
Go to Settings → App Store (or Settings → your name → iTunes & App Store on older labels), then enable App Updates. Your iPhone will download updates in the background when it is charging and on Wi-Fi in most cases.
If an update will not install
Check storage under Settings → General → iPhone Storage. Restart the iPhone, sign out and back into the App Store account if needed, and confirm the date and time are set automatically. If one app fails repeatedly, delete it and reinstall from the App Store after you confirm you will not lose local data you need.
Related reading
See also how to rearrange apps on iPhone and the iOS beginner guide.
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