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/src/python/python.md

@@ -27,8 +27,8 @@ connect, per-table storage and write options on create, and `index_cache_size`,
 Omit these options to use server-managed storage and caching. Connection-level
 `storage_options` supported by an Enterprise deployment remain available.
 
-The synchronous remote `create_table` uses the same positional order as the
-local API: `name, data, schema, mode, exist_ok, on_bad_vectors, fill_value,
+The synchronous LanceDB Distributed `create_table` uses the same positional order as the
+LanceDB Embedded API: `name, data, schema, mode, exist_ok, on_bad_vectors, fill_value,
 embedding_functions`. Prefer keyword arguments for optional parameters.
 
 ## Connections (Synchronous)
@@ -227,14 +227,14 @@ async for entry in catalog.authz.list_acls(subject=Subject.role("reader")):
 
 ## Remote SQL
 
-Submit SQL against a remote LanceDB database through the connection.
+Submit SQL against a LanceDB Distributed database through the connection.
 The connected database and `default_namespace_path=["public"]` are used for
 unqualified tables. Fully qualified references can still query other databases
 and namespaces available to the same deployment. `execute_query` returns a
 reader as soon as its initial result stream is available. `execute_query_async`
 returns a query handle once submission is accepted; use it to inspect progress, open a reader,
 or cancel the query. The SQL client is initialized by the first query and
-retained for the lifetime of the remote connection. Query ids are random,
+retained for the lifetime of the connection. Query ids are random,
 connection-scoped references rather than encoded SQL or durable resume tokens.
 
 Both APIs start with one Flight call. The server can stream results on that
@@ -308,24 +308,24 @@ listing a storage directory.
 
 ## Tables (Synchronous)
 
-Local and remote tables use the same arguments for index creation, deletion,
+LanceDB Embedded and LanceDB Distributed tables use the same arguments for index creation, deletion,
 index statistics, and search. For example, `table.delete(where="id = 1")`,
 `table.create_index("cosine", 2)` (the deprecated vector API), and
 `table.search([1.0, 1.0], fast_search=True)` work with either backend.
 `fast_search=True` excludes rows that have not been indexed.
 
 `create_scalar_index` defaults to `replace=True` on both backends. Both scalar
-and full-text index creation accept `wait_timeout`. Remote maintenance methods
-accept the local options: cleanup and compaction warn that they are no-ops,
+and full-text index creation accept `wait_timeout`. LanceDB Distributed maintenance methods
+accept the LanceDB Embedded options: cleanup and compaction warn that they are no-ops,
 while `optimize` reports an unsupported operation. Removed Tantivy options
 produce the same explanatory errors on both backends.
 
-The old remote keyword names `predicate` for `delete`, `index_name` for
+The old LanceDB Distributed keyword names `predicate` for `delete`, `index_name` for
 `drop_index`, `index_uuid` for `index_stats`, and `column` for `create_fts_index`
 remain available with deprecation warnings. Use `where`, `name`, `index_name`,
 and `field_names`, respectively. For positional calls, use the argument order
 documented by `Table` below; specify index options by keyword when migrating
-code that used the former remote-only argument order.
+code that used the former LanceDB Distributed-only argument order.
 
 ::: lancedb.table.Table
 
@@ -429,14 +429,14 @@ scoped to each invocation and support `read`, `readinto`, `seek`, `tell`,
 
 ## Materialized Views (Synchronous)
 
-In the 0.41 SDK release, local materialized-view creation and refresh require a
+In the 0.41 SDK release, LanceDB Embedded materialized-view creation and refresh require a
 source build with the `experimental-functions` Cargo feature. Published Python
 packages leave it disabled. Opening, reading, listing and dropping existing views
-remain available, as do remote Cloud and Enterprise operations. The same feature
-requirement applies to local SQL computed-column declaration and refresh; ordinary
+remain available, as do LanceDB Distributed operations. The same feature
+requirement applies to LanceDB Embedded SQL computed-column declaration and refresh; ordinary
 eager `add_columns` transforms remain available.
 
-On Cloud and Enterprise, creation accepts `auto_refresh_enabled` and
+In LanceDB Distributed, creation accepts `auto_refresh_enabled` and
 `auto_refresh_interval_seconds`:
 
 ```python
@@ -581,13 +581,13 @@ pylance, LanceDB uses a matching `lance.blob.v2` extension type so blob columns
 still work. Native table queries return descriptors. Call
 [`fetch_blob_files`][lancedb.table.Table.fetch_blob_files] for lazy reads or
 [`fetch_blobs`][lancedb.table.Table.fetch_blobs] for eager bytes.
-Local tables support these fetch APIs for both legacy blob v1 columns
+LanceDB Embedded supports these fetch APIs for both legacy blob v1 columns
 (`lance-encoding:blob`) and blob v2 columns. For legacy columns, obtain row IDs
 with `search().with_row_id(True).to_arrow()` and pass the result to the fetch API.
 One missing or deleted row ID rejects the entire blob-read batch; the APIs do
 not return partial results.
 
-Remote SQL returns blob bytes by default. Select `blob_descriptor(video)` to
+LanceDB Distributed SQL returns blob bytes by default. Select `blob_descriptor(video)` to
 return an openable reference instead, then use
 [`open_blob_file`][lancedb.table.Table.open_blob_file] or the lazy iterable
 [`open_blob_files`][lancedb.table.Table.open_blob_files]:
@@ -604,7 +604,7 @@ for row in rows.to_pylist():
             frame = extract_frame(video, row["timestamp"])
 ```
 
-This example uses a remote SQL connection that produces source-bearing
+This example uses a LanceDB Distributed SQL connection that produces source-bearing
 descriptors. The descriptor contains `kind`, `position`, `size`, `blob_id`,
 `blob_uri`, and a `source` struct with `uri`, `version`, `committed_at_micros`,
 `branch`, `column`, `row_reference`, and `row_is_address`. The opener verifies
@@ -636,7 +636,7 @@ async for video in async_videos.open_blob_files(rows["video"]):
 ```
 
 Payload bytes load on reads. Opening an external blob with unspecified size
-can issue a metadata-only HEAD request. Remote reads use authenticated range
+can issue a metadata-only HEAD request. LanceDB Distributed reads use authenticated range
 requests that validate the captured URI and commit timestamp.
 
 Blobs inside lists can be written and queried as descriptors. They are omitted