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>

nodejs/__test__/remote.test.ts

@@ -115,14 +115,14 @@ describe("remote connection", () => {
             ...options,
             mode: "overwrite",
           }),
-        ).rejects.toThrow(/write_options.*remote/);
+        ).rejects.toThrow(/write_options.*LanceDB Distributed/);
         await expect(
           db.createEmptyTable(
             "test",
             new Schema([new Field("value", new Int64(), true)]),
             options,
           ),
-        ).rejects.toThrow(/write_options.*remote/);
+        ).rejects.toThrow(/write_options.*LanceDB Distributed/);
       },
     );
     expect(requests).toEqual([]);
@@ -140,7 +140,9 @@ describe("remote connection", () => {
         async (db) => {
           await expect(
             db.openTable("test", undefined, options),
-          ).rejects.toThrow(/not supported for remote/);
+          ).rejects.toThrow(
+            /not supported for table access in LanceDB Distributed/,
+          );
         },
       );
       expect(requests).toEqual([]);
@@ -316,7 +318,7 @@ describe("remote connection", () => {
           ],
         ];
         for (const [run, operation] of cases) {
-          let message = `LanceDBError: not supported: ${operation} is not supported for remote tables.`;
+          let message = `LanceDBError: not supported: ${operation} is not supported in LanceDB Distributed.`;
           if (operation === "IVF_HNSW_PQ") {
             message += " Please use IVF_HNSW_SQ instead.";
           }
@@ -463,7 +465,7 @@ describe("remote connection", () => {
           table.add([{ id: 1n }], {
             allowExternalBlobOutsideBases: true,
           }),
-        ).rejects.toThrow("only supported on local tables");
+        ).rejects.toThrow("only supported in LanceDB Embedded");
         expect(insertRequests).toBe(0);
 
         await expect(table.add([{ id: 2n }])).resolves.toMatchObject({

nodejs/__test__/table.test.ts

@@ -4526,14 +4526,14 @@ describe.each(arrowVersions)(
       ];
       const table = await db.createTable("prewarm_data_test", data);
 
-      // prewarmData is only supported on remote tables. We verify the call
+      // prewarmData is only supported in LanceDB Distributed. We verify the call
       // is wired through napi and surfaces the expected error for both
       // arg shapes (undefined and string[]).
       await expect(table.prewarmData()).rejects.toThrow(
-        "prewarm_data is currently only supported on remote tables",
+        "prewarm_data is currently only supported in LanceDB Distributed",
       );
       await expect(table.prewarmData(["text"])).rejects.toThrow(
-        "prewarm_data is currently only supported on remote tables",
+        "prewarm_data is currently only supported in LanceDB Distributed",
       );
     });
 
@@ -5506,7 +5506,7 @@ describe("computed columns", () => {
     const db = await connect(tmpDir.name);
     const table = await db.createTable("errors_local", [{ x: 1 }]);
     await expect(table.functionErrors()).rejects.toThrow(
-      "LanceDB Cloud and Enterprise",
+      "recorded only in LanceDB Distributed",
     );
   });