MCP: Also match against schema names (#3956)

## Changes

`find_tables` does support filtering but right now it only filters table
names and not schemas.

Before:
catalog: `samples`
filter: `*taxi*`
result: nothing 

After:
catalog: `samples`
filter: `*taxi*`
result: samples.nyctaxi.trips

Also contains a critical fix that prevented the find_tables command from
working

## Why
I noticed that claude did struggle to find the table and needed three
round trips to find the right table

## Tests
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Author: fjakobs

experimental/apps-mcp/lib/providers/databricks/databricks.go

@@ -635,7 +635,9 @@ func (c *DatabricksRestClient) ListTables(ctx context.Context, request *ListTabl
 			filterLower := strings.ToLower(*request.Filter)
 			var filtered []TableInfoResponse
 			for _, t := range tables {
-				if strings.Contains(strings.ToLower(t.Name), filterLower) {
+				// Match against both table name and schema name
+				if strings.Contains(strings.ToLower(t.Name), filterLower) ||
+					strings.Contains(strings.ToLower(t.SchemaName), filterLower) {
 					filtered = append(filtered, t)
 				}
 			}
@@ -712,7 +714,8 @@ func (c *DatabricksRestClient) listTablesViaInformationSchema(ctx context.Contex
 			pattern = "%" + pattern + "%"
 		}
 
-		conditions = append(conditions, "table_name LIKE :pattern ESCAPE '\\\\'")
+		// Match against both table name and schema name
+		conditions = append(conditions, "(table_name LIKE :pattern ESCAPE '\\\\' OR table_schema LIKE :pattern ESCAPE '\\\\')")
 		parameters = append(parameters, sql.StatementParameterListItem{
 			Name:  "pattern",
 			Value: pattern,

experimental/apps-mcp/lib/providers/databricks/provider.go

@@ -112,10 +112,18 @@ func (p *Provider) RegisterTools(server *mcpsdk.Server) error {
 	mcpsdk.AddTool(server,
 		&mcpsdk.Tool{
 			Name:        "databricks_find_tables",
-			Description: "Find tables in Databricks Unity Catalog. Supports searching within a specific catalog and schema, across all schemas in a catalog, or across all catalogs. Supports wildcard patterns (* for multiple characters, ? for single character) in table name filtering.",
+			Description: "Find tables in Databricks Unity Catalog. Supports searching within a specific catalog and schema, across all schemas in a catalog, or across all catalogs. Supports wildcard patterns (* for multiple characters, ? for single character) in table name and schema name filtering.",
 		},
 		session.WrapToolHandler(p.session, func(ctx context.Context, req *mcpsdk.CallToolRequest, args FindTablesInput) (*mcpsdk.CallToolResult, any, error) {
-			log.Debugf(ctx, "databricks_find_tables called: catalog=%s, schema=%s", *args.CatalogName, *args.SchemaName)
+			catalogName := "<all>"
+			if args.CatalogName != nil {
+				catalogName = *args.CatalogName
+			}
+			schemaName := "<all>"
+			if args.SchemaName != nil {
+				schemaName = *args.SchemaName
+			}
+			log.Debugf(ctx, "databricks_find_tables called: catalog=%s, schema=%s", catalogName, schemaName)
 
 			client, err := NewDatabricksRestClient(ctx, p.config)
 			if err != nil {