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/feature-engineering/add-computed-column.mdx

@@ -16,9 +16,9 @@ Declaring it is cheap on any table size, because nothing is evaluated until
 [a refresh](/feature-engineering/refresh-column) asks for it.
 
 <Note>
-In the 0.41 SDK release, local computed-column declaration and refresh require a
+In the 0.41 SDK release, computed-column declaration and refresh in LanceDB Embedded require a
 source build with the `experimental-functions` Cargo feature. Published Python
-and TypeScript packages leave it disabled. Remote Cloud and Enterprise operations
+and TypeScript packages leave it disabled. LanceDB Enterprise operations
 do not require this feature. Ordinary eager `add_columns` transforms remain available.
 </Note>
 

docs/web/feature-engineering/index.mdx

@@ -70,7 +70,7 @@ changes incrementally for supported queries; other queries require a full rebuil
 See [refresh behavior](/feature-engineering/materialized-views#incremental) for
 version-specific details.
 
-Enterprise runs materialization on remote compute. Use the SDK and refresh
+Enterprise runs materialization on the Enterprise service. Use the SDK and refresh
 options supported by your server version; see
 [Enterprise refreshes](/feature-engineering/materialized-views#availability).
 
@@ -78,8 +78,8 @@ options supported by your server version; see
 
 | | What it produces | Filled by | Available |
 | --- | --- | --- | --- |
-| [Computed column](/feature-engineering/add-computed-column) | a new column on an existing table | a SQL expression | OSS and Enterprise |
-| [Materialized view](/feature-engineering/materialized-views) | a new table derived by a query | a refresh | OSS and Enterprise |
+| [Computed column](/feature-engineering/add-computed-column) | a new column on an existing table | a SQL expression | Embedded and Enterprise |
+| [Materialized view](/feature-engineering/materialized-views) | a new table derived by a query | a refresh | Embedded and Enterprise |
 | [Geneva](/geneva) | columns filled by Python | the `geneva` package | <Badge color="red">Enterprise</Badge> |
 
 {/*

docs/web/feature-engineering/materialized-views.mdx

@@ -8,7 +8,7 @@ availability:
   oss: available
   enterprise: available
   summary: >-
-    Local creation and refresh require a source build with the experimental-functions Cargo feature. Enterprise runs the work on remote compute. See [Enterprise refreshes](#availability) for server compatibility requirements.
+    Creation and refresh in LanceDB Embedded require a source build with the experimental-functions Cargo feature. Enterprise runs the work on the Enterprise service. See [Enterprise refreshes](#availability) for server compatibility requirements.
 ---
 
 import {
@@ -21,10 +21,10 @@ filtered or transformed dataset that you can query, index and search repeatedly.
 Refresh the view after its source data changes.
 
 <Note>
-In the 0.41 SDK release, local materialized-view creation and refresh require a
+In the 0.41 SDK release, materialized-view creation and refresh in LanceDB Embedded require a
 source build with the `experimental-functions` Cargo feature. Published Python
 and TypeScript packages leave it disabled. Opening, reading, listing and dropping
-existing views remain available, as do remote Cloud and Enterprise operations.
+existing views remain available, as do LanceDB Enterprise operations.
 </Note>
 
 <Note>
@@ -84,7 +84,7 @@ when maintaining an existing pipeline.
 
 <Badge color="red">Enterprise</Badge>
 
-Enterprise runs materialized-view creation and refresh on remote compute.
+Enterprise runs materialized-view creation and refresh on the Enterprise service.
 For SQL, see [`CREATE MATERIALIZED VIEW`](/sql/ddl/materialized-view) and
 [`REFRESH MATERIALIZED VIEW`](/sql/dml/refresh#refresh-materialized-view).
 

docs/web/feature-engineering/refresh-column.mdx

@@ -16,9 +16,9 @@ new rows and recompute values whose inputs changed. The example below continues
 with the `doubled` column from the computed-column guide.
 
 <Note>
-In the 0.41 SDK release, local declaration and refresh require a source build
+In the 0.41 SDK release, declaration and refresh in LanceDB Embedded require a source build
 with the `experimental-functions` Cargo feature. Published Python and TypeScript
-packages leave it disabled. Remote Cloud and Enterprise operations do not require
+packages leave it disabled. LanceDB Enterprise operations do not require
 this feature; existing computed-column data remains readable in default builds.
 </Note>
 
@@ -82,9 +82,9 @@ table.add_columns(
 
 Both options apply to every computed output declared in that call, including
 registered Function outputs. Automatic refresh is enabled by default. When
-the interval is omitted, the server determines when to refresh. Local tables
-persist only an explicitly configured interval; automatic execution requires a
-Cloud or Enterprise server with its separate `column_refresh.enabled` switch
+the interval is omitted, the server determines when to refresh. LanceDB Embedded
+tables persist only an explicitly configured interval; automatic execution requires a
+LanceDB Enterprise deployment with its separate `column_refresh.enabled` switch
 turned on. That server switch is disabled in the base configuration.
 
 The interval is a positive minimum delay after the last successful refresh