docs: make the object-storage connection examples bind db

The quickstart says the TypeScript and Rust code of steps 2 to 5 makes one
program, whichever connection the reader picks. The object-storage examples
broke that: the TypeScript one defined an uncalled function whose db was
local to it and had no import, and the Rust one declared uri but never
connected. Both now bind db in the program's scope, as the local and
Enterprise examples do, and the quickstart shows their import lines. The test
functions that hold them stay uncalled, so no test reaches object storage. The
connection guide shows the TypeScript example with its import line too.

docs/web-tests/rs/connection.rs

@@ -37,7 +37,6 @@ async fn main() -> Result<(), Box<dyn std::error::Error>> {
         let db = connect_enterprise_quickstart().await?;
         println!("{:?}", db.table_names().execute().await?);
     }
-    let _ = connect_object_storage_config();
     Ok(())
 }
 
@@ -58,13 +57,15 @@ async fn connect_enterprise_quickstart() -> Result<Connection, Box<dyn std::erro
     Ok(db)
 }
 
-fn connect_object_storage_config() -> &'static str {
+// Compiled as documentation, never called by the example runner.
+#[allow(dead_code)]
+async fn connect_object_storage() -> lancedb::Result<Connection> {
     // --8<-- [start:connect_object_storage]
     let uri = "s3://your-bucket/path";
     // You can also use "gs://your-bucket/path" or "az://your-container/path".
+    let db = connect(uri).execute().await?;
     // --8<-- [end:connect_object_storage]
-
-    uri
+    Ok(db)
 }
 
 async fn namespace_table_ops_example(uri: &str) -> lancedb::Result<()> {

docs/web-tests/ts/connection.test.ts

@@ -76,14 +76,14 @@ describe("enterprise quickstart connect", () => {
   });
 });
 
-// --8<-- [start:connect_object_storage]
 async function connectObjectStorageExample() {
+  // --8<-- [start:connect_object_storage]
   const uri = "s3://your-bucket/path";
   // You can also use "gs://your-bucket/path" or "az://your-container/path".
   const db = await lancedb.connect(uri);
+  // --8<-- [end:connect_object_storage]
   return db;
 }
-// --8<-- [end:connect_object_storage]
 
 async function namespaceTableOpsExample() {
   // --8<-- [start:namespace_table_ops]

docs/web/basics/connect.mdx

@@ -71,6 +71,7 @@ covers credentials, endpoints and provider options.
     </CodeBlock>
 
     <CodeBlock filename="TypeScript" language="TypeScript" icon="square-js">
+    { "import * as lancedb from \"@lancedb/lancedb\";\n\n" }
     {TsConnectObjectStorage}
     </CodeBlock>
 </CodeGroup>

docs/web/quickstart.mdx

@@ -192,10 +192,13 @@ You can also connect directly to object storage from the client SDK:
     </CodeBlock>
 
     <CodeBlock filename="TypeScript" language="TypeScript" icon="square-js">
+    { "import * as lancedb from \"@lancedb/lancedb\";\n\n" }
     {TsConnectObjectStorage}
     </CodeBlock>
 
     <CodeBlock filename="Rust" language="Rust" icon="rust">
+    { "use lancedb::connect;\n" }
+    { "\n" }
     {RsConnectObjectStorage}
     </CodeBlock>
 </CodeGroup >

docs/web/snippets/connection.mdx

@@ -18,7 +18,7 @@ export const TsConnect = "const db = await lancedb.connect(\"ex_lancedb\");\n";
 
 export const TsConnectEnterpriseQuickstart = "const setting = (name: string) => {\n  const value = process.env[name];\n  if (!value) throw new Error(`Set ${name}`);\n  return value;\n};\n\nconst db = await lancedb.connect(setting(\"LANCEDB_URI\"), {\n  apiKey: setting(\"LANCEDB_API_KEY\"),\n  region: process.env.LANCEDB_REGION ?? \"us-east-1\",\n  hostOverride: setting(\"LANCEDB_HOST_OVERRIDE\"),\n});\n";
 
-export const TsConnectObjectStorage = "async function connectObjectStorageExample() {\n  const uri = \"s3://your-bucket/path\";\n  // You can also use \"gs://your-bucket/path\" or \"az://your-container/path\".\n  const db = await lancedb.connect(uri);\n  return db;\n}\n";
+export const TsConnectObjectStorage = "const uri = \"s3://your-bucket/path\";\n// You can also use \"gs://your-bucket/path\" or \"az://your-container/path\".\nconst db = await lancedb.connect(uri);\n";
 
 export const TsNamespaceAdminOps = "const db = await lancedb.connectNamespace(\"dir\", { root: \"./local_lancedb\" });\nconst namespace = [\"prod\", \"search\"];\n\nawait db.createNamespace([\"prod\"]);\nawait db.createNamespace([\"prod\", \"search\"]);\n\nconst childNamespaces = (await db.listNamespaces([\"prod\"])).namespaces;\nconsole.log(`Child namespaces under ${JSON.stringify(namespace)}:`, childNamespaces);\n// Child namespaces under [\"prod\",\"search\"]: [ 'search' ]\n\nconst metadata = await db.describeNamespace([\"prod\", \"search\"]);\nconsole.log(`Metadata for namespace ${JSON.stringify(namespace)}:`, metadata);\n\nawait db.dropNamespace([\"prod\", \"search\"], { mode: \"skip\" });\nawait db.dropNamespace([\"prod\"], { mode: \"skip\" });\n";
 
@@ -28,7 +28,7 @@ export const RsConnect = "let db = connect(\"ex_lancedb\").execute().await?;\n";
 
 export const RsConnectEnterpriseQuickstart = "let uri = std::env::var(\"LANCEDB_URI\")?; // db://your-database\nlet api_key = std::env::var(\"LANCEDB_API_KEY\")?;\nlet region = std::env::var(\"LANCEDB_REGION\").unwrap_or_else(|_| \"us-east-1\".to_string());\nlet host_override = std::env::var(\"LANCEDB_HOST_OVERRIDE\")?; // https://your-endpoint\n\nlet db = connect(&uri)\n    .api_key(&api_key)\n    .region(&region)\n    .host_override(&host_override)\n    .execute()\n    .await?;\n";
 
-export const RsConnectObjectStorage = "let uri = \"s3://your-bucket/path\";\n// You can also use \"gs://your-bucket/path\" or \"az://your-container/path\".\n";
+export const RsConnectObjectStorage = "let uri = \"s3://your-bucket/path\";\n// You can also use \"gs://your-bucket/path\" or \"az://your-container/path\".\nlet db = connect(uri).execute().await?;\n";
 
 export const RsNamespaceAdminOps = "let mut properties = std::collections::HashMap::new();\nproperties.insert(\"root\".to_string(), \"./local_lancedb\".to_string());\nlet db = lancedb::connect_namespace(\"dir\", properties).execute().await?;\nlet namespace = vec![\"prod\".to_string(), \"search\".to_string()];\n\ndb.create_namespace(lance_namespace::models::CreateNamespaceRequest {\n    id: Some(vec![\"prod\".to_string()]),\n    ..Default::default()\n})\n.await?;\ndb.create_namespace(lance_namespace::models::CreateNamespaceRequest {\n    id: Some(namespace.clone()),\n    ..Default::default()\n})\n.await?;\n\nlet child_namespaces = db\n    .list_namespaces(lance_namespace::models::ListNamespacesRequest {\n        id: Some(vec![\"prod\".to_string()]),\n        ..Default::default()\n    })\n    .await?;\nprintln!(\n    \"Child namespaces under {:?}: {:?}\",\n    namespace, child_namespaces\n);\n// Child namespaces under [\"prod\", \"search\"]: [\"search\"]\n\ndb.drop_namespace(lance_namespace::models::DropNamespaceRequest {\n    id: Some(namespace.clone()),\n    ..Default::default()\n})\n.await?;\ndb.drop_namespace(lance_namespace::models::DropNamespaceRequest {\n    id: Some(vec![\"prod\".to_string()]),\n    ..Default::default()\n})\n.await?;\n";