feat(perplexity): add PerplexityEmbeddings (#37082)

## Description

This PR adds a new `PerplexityEmbeddings` class to the
`langchain-perplexity` partner package, providing first-class support
for the Perplexity Embeddings API alongside the existing
`ChatPerplexity`, `PerplexitySearchRetriever`, and
`PerplexitySearchResults` integrations.

### What was added

- `langchain_perplexity/embeddings.py` — `PerplexityEmbeddings` class
implementing `langchain_core.embeddings.Embeddings` with sync
(`embed_documents`, `embed_query`) and async (`aembed_documents`,
`aembed_query`) methods. Defaults to model `pplx-embed-v1-4b` and reuses
the existing `_utils.initialize_client` helper for API key resolution
(`PPLX_API_KEY` / `PERPLEXITY_API_KEY`).
- `__init__.py` exports `PerplexityEmbeddings` and adds it to `__all__`.
- Unit tests under `tests/unit_tests/test_embeddings.py` covering
sync/async paths with mocked clients (no network).
- Integration tests under `tests/integration_tests/test_embeddings.py`,
gated on `PPLX_API_KEY` (matches the pattern in `test_search_api.py`).
- README updated to advertise the new component.

### Why

LangChain users already get chat, search, and tool wrappers from
`langchain-perplexity`, but had to drop down to the raw Perplexity SDK
to use embeddings. This closes that gap.

### References

- Perplexity Embeddings docs: https://docs.perplexity.ai/docs/embeddings
- Perplexity Embeddings API reference:
https://docs.perplexity.ai/api-reference/embeddings-post

### Issue

Closes #36726

## Testing

- `cd libs/partners/perplexity && make lint` — passes (ruff, format,
mypy).
- `cd libs/partners/perplexity && make test` — all unit tests pass (59
passed, 1 skipped).
- Integration tests will run in CI with secrets; they exercise real
`embed_documents` / `embed_query` / async variants against the live API
and assert vector dimensionality consistency.

---------

Co-authored-by: Claude Agent <agent@anthropic.com>
Co-authored-by: Mason Daugherty <github@mdrxy.com>

libs/partners/perplexity/tests/integration_tests/test_embeddings.py

@@ -0,0 +1,56 @@
+"""Integration tests for Perplexity Embeddings API."""
+
+import os
+
+import pytest
+
+from langchain_perplexity import PerplexityEmbeddings
+
+
+@pytest.mark.skipif(
+    not (os.environ.get("PPLX_API_KEY") or os.environ.get("PERPLEXITY_API_KEY")),
+    reason="PPLX_API_KEY/PERPLEXITY_API_KEY not set",
+)
+class TestPerplexityEmbeddings:
+    def test_embed_documents(self) -> None:
+        """Test embedding a list of documents."""
+        embeddings = PerplexityEmbeddings()
+        texts = ["hello world", "goodbye world"]
+        vectors = embeddings.embed_documents(texts)
+
+        assert len(vectors) == len(texts)
+        assert all(isinstance(v, list) for v in vectors)
+        assert all(len(v) > 0 for v in vectors)
+        # All vectors should have the same dimensionality.
+        assert len({len(v) for v in vectors}) == 1
+        assert all(isinstance(x, float) for x in vectors[0])
+
+    def test_embed_query(self) -> None:
+        """Test embedding a single query."""
+        embeddings = PerplexityEmbeddings()
+        vector = embeddings.embed_query("What is the capital of France?")
+
+        assert isinstance(vector, list)
+        assert len(vector) > 0
+        assert all(isinstance(x, float) for x in vector)
+
+    def test_embed_query_matches_documents_dim(self) -> None:
+        """Embeddings from query and documents should share dimensionality."""
+        embeddings = PerplexityEmbeddings()
+        query_vec = embeddings.embed_query("hello")
+        doc_vecs = embeddings.embed_documents(["hello"])
+        assert len(query_vec) == len(doc_vecs[0])
+
+    async def test_aembed_documents(self) -> None:
+        """Test async embedding a list of documents."""
+        embeddings = PerplexityEmbeddings()
+        vectors = await embeddings.aembed_documents(["hello", "world"])
+        assert len(vectors) == 2
+        assert all(len(v) > 0 for v in vectors)
+
+    async def test_aembed_query(self) -> None:
+        """Test async embedding a single query."""
+        embeddings = PerplexityEmbeddings()
+        vector = await embeddings.aembed_query("hello")
+        assert isinstance(vector, list)
+        assert len(vector) > 0

libs/partners/perplexity/tests/integration_tests/test_embeddings_standard.py

@@ -0,0 +1,23 @@
+"""Standard integration tests for `PerplexityEmbeddings`."""
+
+import os
+
+import pytest
+from langchain_core.embeddings import Embeddings
+from langchain_tests.integration_tests import EmbeddingsIntegrationTests
+
+from langchain_perplexity import PerplexityEmbeddings
+
+
+@pytest.mark.skipif(
+    not (os.environ.get("PPLX_API_KEY") or os.environ.get("PERPLEXITY_API_KEY")),
+    reason="PPLX_API_KEY/PERPLEXITY_API_KEY not set",
+)
+class TestPerplexityEmbeddingsIntegration(EmbeddingsIntegrationTests):
+    @property
+    def embeddings_class(self) -> type[Embeddings]:
+        return PerplexityEmbeddings
+
+    @property
+    def embedding_model_params(self) -> dict:
+        return {}