refactor: only prevent mousedown on mobile if input has focus

[web-padawan]

Description

Fixes #10149

WIP, still need to do:

• more testing on real mobile devices (especially iOS) to verify possible timing issues
• tweaks in date-picker to not blur input on clear button when overlay contains focus.

Type of change

• Refactor / bugfix

Note

There was a problem with testing on iOS device, see recording below:

• Second field has focus, clearing first field - works (field loses focus as expected)
• First field has focus, clearing second field - broken (focus stays in the first field)

ScreenRecording_09-25-2025.12-55-21_1.MP4

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud