Fix mobile date picker display and instant search behavior

[RabbiIslamRony]

PR Type

What kind of change does this PR introduce?

• Bugfix
• Security fix
• Improvement
• New Feature
• Refactoring (no functional changes, no api changes)
• Build related changes
• Text changes
• Other... Please describe:

Description

How to reproduce the issue or how to test the changes

1. Open the All Listings page for a directory containing a date search field, then switch to a mobile viewport or use an Android/iOS device.
2. Confirm the empty date field displays the Date label without overlapping the browser's native date template.
3. Select a date on Android and confirm instant search runs after the native picker commits the value.
4. Select a date on iOS and confirm the native picker remains open until focus leaves the field, then instant search runs.
5. Confirm a failed instant-search AJAX request falls back to loading the filtered URL instead of leaving stale listing results.
6. Confirm desktop date-field presentation remains unchanged.

Validation completed:

• npm run build-legacy passed with existing asset-size warnings.
• git diff --check passed.
• Empty, focused, selected, instant-search, 440px mobile, and 1440px desktop states were browser-tested.
• Generated build files are intentionally excluded from this PR.

Any linked issues

Fixes #
https://team.sovware.com/support/directorist/3159

Checklist

• My code follows the WordPress coding standards