Implement database object search functionality for improved navigation in large schemas

Problem:

When working with databases containing hundreds of tables/objects, the current explorer interface becomes inefficient:

• No way to quickly find specific objects (tables, views, functions) by name
• Requires manual expansion of schema trees, causing visual clutter and slowdowns
• Significantly reduces productivity during development and debugging

Requested Solution:

Add a search bar to the database explorer (inspired by Azure Data Studio) with:

1. Real-time filtering: Instant display of matching objects across all schemas as users type
2. Case-insensitive partial matching: e.g. typing order shows Orders, public.order_details, tbl_orders_2024
3. Type filtering: Ability to search specific object types:
   • Tables
   • Views
   • Functions/Procedures
   • Indexes
   • Other database objects
4. Clean UI: Position search bar above schema tree with collapsible results

Mockup:

[ 🔍 Search objects... ]  <-- New search bar
├─ Schemas
   ├─ public             
   │  └─ orders          <-- Only visible when matching
   └─ hr  
      └─ employees       <-- Only visible when matching

Why This Is Important:

• Time savings: Instantly locate objects like payment_history without scanning through hundreds of objects across multiple schemas
• Industry standard: Matching functionality exists in Azure Data Studio, DBeaver, and DataGrip
• Essential for large databases: Critical when working with complex databases containing thousands of objects distributed across numerous schemas

No files, tests, or entry points are named in the issue. Start by locating the database explorer implementation and its schema/object loading and rendering paths, then determine how search and object-type filtering would fit across schemas. Done means a responsive, case-insensitive search bar filters the specified object types and preserves a usable schema-tree presentation.