docs: adopt Embedded/Distributed terminology across docs and SDKs (#4713)

## Summary

Adopts the product terminology guide across the docs site pages, SDK
docstrings and error messages. "LanceDB OSS" and local mode become
**LanceDB Embedded**. "Remote" as the execution model becomes **LanceDB
Distributed**, which LanceDB Enterprise provides. Where free vs paid is
the point, pages contrast "LanceDB Embedded (open source)" with "LanceDB
Enterprise". This is a first trial of the Embedded name, so reviewers
can judge it in context.

- **Embedded vs Distributed** for where execution runs (`optimize()`,
consistency, branching, maintenance). Main pages define it once:
"LanceDB Enterprise runs LanceDB Distributed: …"
- **LanceDB Cloud** is kept only for legacy-Cloud specifics (`db://`
region, the brute-force KNN limit) and marked legacy. "Cloud and
Enterprise" becomes Enterprise or Distributed.
- **Plan executor** becomes "executor" or the fleet name.
- **Error messages** change, e.g. `optimize is not supported for remote
tables.` → `... in LanceDB Distributed.` Tests that match on them are
updated.
- **Vale rules** (`EmbeddedName`, `OSSProduct`, `RemoteExecution`,
`DistributedEnterprise`, `LegacyCloud`, `InternalNames`) enforce the
terms in prose.

Unchanged: identifiers (`availability.oss`, the `remote` module and
feature, `RemoteTable`, `db://`), heading anchors, internal code
comments, and Geneva.

## Evidence

- Rust lib tests for the changed messages and the Python tests in
`test_remote_db.py`, `test_materialized_views.py` and `test_table.py`
pass locally.
- Not run locally:
- The Node tests: `remote.test.ts` and `table.test.ts` have updated
assertions.
  - Vale.
  - The `experimental_functions`-marked materialized-view tests.
- `docs/src` API reference was hand-edited to match the docstrings
rather than regenerated.

## Merge Risk

**Door:** two-way; prose and message text only.
**Blast Radius:** `docs`, `error-messages`: callers matching on old
error strings would break.

Companion PRs: lancedb/docs (assembler labels, STYLE.md) and sophon
(Enterprise pages).

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>

docs/web/integrations/data/dlt.mdx

@@ -40,7 +40,7 @@ In this example, we will be fetching movie information from the [Open Movie Data
 
 3. **Specify necessary credentials and/or embedding model details:**  
     
-    To fetch data from the OMDb API, you will need to pass a valid API key into your pipeline. Depending on whether you're using LanceDB OSS or LanceDB Enterprise, you also may need to provide the necessary credentials to connect to the LanceDB instance. These can be pasted inside `.dlt/secrets.toml`.
+    To fetch data from the OMDb API, you will need to pass a valid API key into your pipeline. Depending on whether you're using LanceDB Embedded or LanceDB Enterprise, you also may need to provide the necessary credentials to connect to the LanceDB instance. These can be pasted inside `.dlt/secrets.toml`.
 
     dlt's LanceDB integration also allows you to automatically embed the data during ingestion. Depending on the embedding model chosen, you may need to paste the necessary credentials inside `.dlt/secrets.toml`:
     ```toml
@@ -52,7 +52,7 @@ In this example, we will be fetching movie information from the [Open Movie Data
     embedding_model = "all-MiniLM-L6-v2"
     [destination.lancedb.credentials]
     uri = ".lancedb"
-    api_key = "api_key" # API key to connect to LanceDB Enterprise. Leave out if you are using LanceDB OSS.
+    api_key = "api_key" # API key to connect to LanceDB Enterprise. Leave out if you are using LanceDB Embedded.
     embedding_model_provider_api_key = "embedding_model_provider_api_key" # Not needed for providers that don't need authentication (ollama, sentence-transformers).
     ```
     See [here](https://dlthub.com/docs/dlt-ecosystem/destinations/lancedb#configure-the-destination) for more information and for a list of available models and model providers.  

docs/web/integrations/data/duckdb.mdx

@@ -6,7 +6,7 @@ description: "Learn how to use the DuckDB-Lance extension to query Lance tables
 
 LanceDB integrates with [DuckDB](https://duckdb.org/) through the [Lance extension](https://github.com/lance-format/lance-duckdb) for DuckDB. In this page, we'll show how LanceDB manages table lifecycle, and DuckDB provides SQL analytics (including joins) and search over those tables.
 
-Note that earlier versions of LanceDB used to recommend converting Lance tables to Arrow tables via `table.to_arrow()`. Although this method is still available for local tables (because DuckDB [natively scans Arrow tables](https://duckdb.org/2021/12/03/duck-arrow)), it is no longer the recommended workflow for working with Lance tables in DuckDB. This page shows how to use the Lance extension with namespace-attached LanceDB tables, allowing you to pushdown SQL queries directly to the Lance layer.
+Note that earlier versions of LanceDB used to recommend converting Lance tables to Arrow tables via `table.to_arrow()`. Although this method is still available for LanceDB Embedded tables (because DuckDB [natively scans Arrow tables](https://duckdb.org/2021/12/03/duck-arrow)), it is no longer the recommended workflow for working with Lance tables in DuckDB. This page shows how to use the Lance extension with namespace-attached LanceDB tables, allowing you to pushdown SQL queries directly to the Lance layer.
 
 
 ## Install {#install}

docs/web/integrations/data/polars_arrow.mdx

@@ -43,7 +43,7 @@ Run vector search and keep the results as a Polars `DataFrame` for further proce
 
 ## Work with LazyFrames {#work-with-lazyframes}
 
-When you want to operate on the entire table (potentially larger than RAM), convert to a Polars `LazyFrame` so you can chain transformations without loading everything at once. This works for local tables only; with LanceDB Enterprise, `search(...).to_polars()` returns an eager DataFrame of query results.
+When you want to operate on the entire table (potentially larger than RAM), convert to a Polars `LazyFrame` so you can chain transformations without loading everything at once. This works for LanceDB Embedded tables only; with LanceDB Enterprise, `search(...).to_polars()` returns an eager DataFrame of query results.
 
 <CodeBlock filename="Python" language="Python" icon="python">
   {PyPlatformsPolarsLazyframe}