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/management/function.mdx

@@ -8,7 +8,7 @@ availability:
   oss: unavailable
   enterprise: available
   summary: >-
-    Enterprise supports Functions when enabled for your Enterprise cluster; the embedded library cannot register or run them.
+    Enterprise supports Functions when enabled for your Enterprise cluster; LanceDB Embedded cannot register or run them.
 ---
 
 import {
@@ -31,8 +31,8 @@ rather than pulling rows to your process.
 
 Registering and running a function needs a LanceDB Enterprise deployment with
 Functions enabled, which they are not by default. On a
-local connection `create_function` raises `NotImplementedError`; to derive a
-column locally, declare a
+LanceDB Embedded connection `create_function` raises `NotImplementedError`; to
+derive a column there, declare a
 [SQL computed column](/feature-engineering/add-computed-column) instead.
 
 <Note>
@@ -282,14 +282,15 @@ as `bytes`; this feature does not add streamed outputs.
 
 ## Declare the environment {#environment}
 
-The function runs remotely, so its dependencies are part of its definition:
+The function runs on the Enterprise service, not in your application, so its
+dependencies are part of its definition:
 
 | | |
 | --- | --- |
-| `pip` | requirements for the remote environment |
+| `pip` | requirements for the function's execution environment |
 | `conda`, `conda_channels` | conda packages instead of pip; channels in priority order |
 | `env` | environment variables |
-| `python_version` | remote Python major/minor, defaulting to yours |
+| `python_version` | Python major/minor for the execution environment, defaulting to yours |
 | `gpu` | whether every execution requires a GPU |
 
 These are part of the **immutable function version**. Changing a dependency