feat(core): drive the unified search modal from the search controller

[pringelmann]

• Resolves: Vue adapter + wire the loading controller into the modal #61928

Summary

Moves search orchestration out of the modal and into UnifiedSearchController, wired up through a new useUnifiedSearch composable. The modal now just renders the controller's per-category state.

-> Preview link <-

Per-category filter params (date, person, provider) are forwarded so filters page correctly on "Load more".

Checklist

• Code is properly formatted
• Sign-off message is added to all commits
• Tests (unit, integration, api and/or acceptance) are included
• Screenshots before/after for front-end changes (preview link)
• Documentation (manuals or wiki) has been updated or is not required
• Backports requested where applicable (ex: critical bugfixes)
• Labels added where applicable (ex: bug/enhancement, 3. to review, feature component)
• Milestone added for target branch/version (ex: 32.x for stable32)

AI (if applicable)

• The content of this PR was partly or fully generated using AI (mostly tests)

[pringelmann]

The controller now takes one onChange callback. I opted for this approach to keep things simple (instead of an event bus or a store). There's a single owner and a single consumer: useUnifiedSearch creates the controller, adapts the callback to a shallowRef, and disposes it on unmount. A callback keeps the controller plain TS with no framework dependency, so it unit-tests without mounting Vue. Pub/sub would add subscriber bookkeeping for listeners that don't exist, and a store would pull in reactivity the core doesn't need.

Happy to debate :)