fix(auth): stabilize phone input editing and country codes

[SecondThundeR]

Fix phone input omitting the displayed country code when typing, duplicated dial codes in placeholders, and inconsistent editing behavior.

• Separate stored phone values from display formatting to preserve cursor positions, selections, and digits.
• Insert the selected dial code for national input while preserving international numbers.
• Keep national digits when changing countries.
• Correct shared-code detection and remember the exact country-picker entry.
• Preserve a typed + and handle the configured IME action.

Validation:

• 138 unit tests passed across core/common and auth.
• All 9 phone-input interaction tests passed on Pixel 10 Pro XL.
• Debug app and instrumentation APK builds passed.

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Developed with assistance from GPT-6.1-Sol (High).