I want to delete apps from my phone, not just the home screen.

If the app is on a Home screen, touch and hold the app, tap Remove app and then tap Delete App (or tap Edit Home Screen in the pop up menu, tap the minus sign, then tap Delete App)

If the app is only in the App Library screen (swipe left past the last Home screen), touch and hold the app there and then tap Delete app.

Note that some built-in Apple apps cannot be deleted.

If neither of those options is available, there may be a restriction set on deleting apps. On an iPhone or iPad, go to Settings > Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases > Deleting Apps.

See: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support

Also be aware that deleting an app does not cancel any related subscriptions. To do that, see: If you want to cancel a subscription from Apple - Apple Support