## Problem
When users trigger actions such as deleting an item, the storage
explorer reloads the opened folders but ignore the currently applied
filter.
## Solution
Move the filter state in Valtio so that its other functions are aware of
it.
## Review instructions
1. Create a Supabase project and upload objects in Storage with date
prefixes (e.g., 202608XX)
2. Navigate to Storage, select a bucket with multi-dated/prefixed
objects
3. Enter a filter in the search box (e.g., 20260820) to show only
matching objects
4. Select one or more filtered objects and delete them
Observe the file list after deletion - it should show filtered contents
according to the search box value
<!-- This is an auto-generated comment: release notes by coderabbit.ai
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## Summary by CodeRabbit
* **Bug Fixes**
* Storage search now stays in sync as you open folders and refresh their
contents.
* When restoring open folders, search results are filtered in the
deepest open folder rather than hiding ancestor folders.
* Deleting a file from filtered results keeps the search applied and
displays the remaining matches correctly.
* Search results remain consistent across folder navigation, refreshes,
and file deletion.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->
Gildas Garcia
5de3666930