How can I customize what apps can give me notifications? For example, I have an app that reminds me to lock my house, and I can't recieve that if the notifications are blocked.

Hi a69a420,

Welcome to the Apple Community.

Re: How can I customize what apps can give me notifications?

With iOS 15 and iPadOS 15 or later, you can turn on Critical Alerts for supported apps

so notifications come through even if your iPhone is muted or you have a Focus set up.

How to: Use notifications on your iPhone or iPad - Apple Support

For iOS 16 : How to: Manage weather notifications on iPhone – Apple Support

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Re: How can I customize what apps can give me notifications in the Driving Focus?

The Driving Focus "Related Article" above your Question

says:

Customize your notifications

To allow or silence notifications from certain people:

✽. Go to Settings > Focus, then tap Driving.

✽. Under Allowed Notifications, tap People.

✽. Tap Allow Notifications From or Silence Notifications From.

✽. Tap Add People, then select the contacts that you want to allow or silence notifications from.

All the best :-)