[pickers] Support For Backspace behavior in Date input clears only part of the year instead of the full year

[AravinthK820]

When a date is selected (e.g. 12/12/2000) and displayed in the input field, placing the cursor at the end of the input and pressing Backspace does not clear the year correctly.

Current behavior:

• Selected date: 12/12/2000
• Cursor placed at the end of the input
• Pressing Backspace once changes the value to:
  12/12/0200
• The year is partially modified instead of being fully cleared.
• Only after the year becomes fully selected does pressing Backspace clear the entire year.

Expected behavior:

• On the first Backspace press, the entire year (YYYY) should be cleared.
• Result should be:
  12/12/YYYY

This behavior is inconsistent with typical date input editing expectations and can be confusing for users.

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Steps to Reproduce

1. Select a date (e.g. 12/12/2000) using the MUI Date Picker.
2. Focus the input field.
3. Place the cursor at the end of the date value.
4. Press Backspace once.

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Expected Result

• The year portion (YYYY) is cleared immediately.

Actual Result

• The year changes to 0200 instead of being fully cleared.

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Environment

• MUI version: 8.2.30
• Browser: Chrome
• React version: 19^