Replace country_pickers to an updated package

## Environment

**Package name:** form_builder_phone_field
**Package version:** 1.0.0-beta.0
**Platform:** All
**Device information:** N/A

## Description

**What you'd like to happen:** Replace dependency country_pickers, because these package don't receive more update

**Alternatives you've considered:**

- https://github.com/Daniel-Ioannou/flutter_country_picker
- https://github.com/dev-naiksan/country-calling-code-picker
- https://github.com/imtoori/CountryCodePicker
- https://github.com/hifiaz/country-list-pick

Review how form_builder_phone_field currently depends on and uses country_pickers, then compare the listed replacement packages: flutter_country_picker, country-calling-code-picker, CountryCodePicker, and country-list-pick. Done means selecting a supported replacement and updating the package so its existing phone-field behavior remains available.

Written by the indexing model from the issue text.