feat: clarify active board filters

[bionicman]

Description

Board filters currently show only a total count on the Filter button. The
dropdown does not indicate which groups contain selected values, and clearing
filters is hidden behind a hover interaction on the count badge.

This change:

• shows the selected-value count next to each filter group;
• keeps the total badge as a status indicator instead of a hidden action;
• adds an explicit Clear filters action at the bottom of the menu;
• adds a back row for moving between filter groups without reopening the menu;
• extends the existing board-filter E2E scenario to cover the count, selected
  checkbox and clear action.

Filter state and behavior are unchanged. The existing URL query remains the
source of truth, and the shared dropdown only gains optional presentation
slots.

Type of change

• Bug fix
• Feature (requires an approved issue — see below)
• Refactor / chore
• Documentation

Screenshots

Group counts and explicit reset, desktop:

Selected value inside a group, desktop:

Group counts and explicit reset, mobile:

Checklist

• I have linked the related issue below
• My code follows the existing style and conventions
• I have tested my changes locally
• I have included screenshots for any UI changes

Linked issue

Closes #580