Add search to application allow list for last notification sensor

**Is your feature request related to a problem? Please describe.**

Related to #3683

The dialog for selecting allowed applications for the last notification sensor can be very large. Working through the list to find an single app can be quite difficult, especially when they are ordered by app ID.

**Describe the solution you'd like**

A search would be very useful to allow the list to be filtered to specific terms. In combination with #3683, apps should be much easier to find.

**Describe alternatives you've considered, if any**

Can look up the ID of the app first by browsing to the google play store page and looking at the URL. That determines it's alphabetical position in the list and makes it easier to find.

**Additional context**

Companion app version: 2023.7.5-full
HA Version: 2023.7.1

Locate the Android dialog that selects allowed applications for the last notification sensor and read how its application list is populated. Check the related work in #3683 for context, then determine how search terms should filter the list. Done means users can enter terms and see matching applications in the allow-list dialog.

Written by the indexing model from the issue text.