docs: Add FAISS Filter with Advanced Query Operators Documentation & Demonstration (#28938)

## Description
This pull request updates the documentation for FAISS regarding filter
construction, following the changes made in commit `df5008f`.

## Issue
None. This is a follow-up PR for documentation of
[#28207](#28207)

## Dependencies:
None.

---------

Co-authored-by: Chester Curme <[email protected]>

Author: RuofanChen03

docs/docs/integrations/vectorstores/faiss.ipynb

@@ -286,6 +286,52 @@
     "    print(f\"* {res.page_content} [{res.metadata}]\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "39cb1496",
+   "metadata": {},
+   "source": [
+    "Some [MongoDB query and projection operators](https://www.mongodb.com/docs/manual/reference/operator/query/) are supported for more advanced metadata filtering. The current list of supported operators are as follows:\n",
+    "- `$eq` (equals)\n",
+    "- `$neq` (not equals)\n",
+    "- `$gt` (greater than)\n",
+    "- `$lt` (less than)\n",
+    "- `$gte` (greater than or equal)\n",
+    "- `$lte` (less than or equal)\n",
+    "- `$in` (membership in list)\n",
+    "- `$nin` (not in list)\n",
+    "- `$and` (all conditions must match)\n",
+    "- `$or` (any condition must match)\n",
+    "- `$not` (negation of condition)\n",
+    "\n",
+    "Performing the same above similarity search with advanced metadata filtering can be done as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1b3dd99d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "* Building an exciting new project with LangChain - come check it out! [{'source': 'tweet'}]\n",
+      "* LangGraph is the best framework for building stateful, agentic applications! [{'source': 'tweet'}]\n"
+     ]
+    }
+   ],
+   "source": [
+    "results = vector_store.similarity_search(\n",
+    "    \"LangChain provides abstractions to make working with LLMs easy\",\n",
+    "    k=2,\n",
+    "    filter={\"source\": {\"$eq\": \"tweet\"}},\n",
+    ")\n",
+    "for res in results:\n",
+    "    print(f\"* {res.page_content} [{res.metadata}]\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "5ae35069",

docs/docs/integrations/vectorstores/faiss_async.ipynb

@@ -397,6 +397,49 @@
     "    print(f\"Content: {doc.page_content}, Metadata: {doc.metadata}\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "8dead085",
+   "metadata": {},
+   "source": [
+    "Some [MongoDB query and projection operators](https://www.mongodb.com/docs/manual/reference/operator/query/) are supported for more advanced metadata filtering. The current list of supported operators are as follows:\n",
+    "- `$eq` (equals)\n",
+    "- `$neq` (not equals)\n",
+    "- `$gt` (greater than)\n",
+    "- `$lt` (less than)\n",
+    "- `$gte` (greater than or equal)\n",
+    "- `$lte` (less than or equal)\n",
+    "- `$in` (membership in list)\n",
+    "- `$nin` (not in list)\n",
+    "- `$and` (all conditions must match)\n",
+    "- `$or` (any condition must match)\n",
+    "- `$not` (negation of condition)\n",
+    "\n",
+    "Performing the same above similarity search with advanced metadata filtering can be done as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "af47c6f9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Content: foo, Metadata: {'page': 1}\n"
+     ]
+    }
+   ],
+   "source": [
+    "results = await db.asimilarity_search(\n",
+    "    \"foo\", filter={\"page\": {\"$eq\": 1}}, k=1, fetch_k=4\n",
+    ")\n",
+    "for doc in results:\n",
+    "    print(f\"Content: {doc.page_content}, Metadata: {doc.metadata}\")"
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "1becca53",