docs: Add schema qualified object references throughout the docs (supabase#39904)

* Update vector type

* Update http and postgis

* Missed a spot on Postgis

* convert the gis reference to extensions in postgis guide

Author: dshukertjr

apps/docs/content/guides/ai/engineering-for-scale.mdx

@@ -110,7 +110,7 @@ We can now create a foreign table to access the data in our secondary project.
 ```sql
 create foreign table docs (
   id text not null,
-  embedding vector(384),
+  embedding extensions.vector(384),
   metadata jsonb,
   url text
 )

apps/docs/content/guides/ai/examples/mixpeek-video-search.mdx

@@ -84,7 +84,7 @@ def seed():
         "id": "text",
         "start_time": "float8",
         "end_time": "float8",
-        "embedding": "vector(768)",
+        "embedding": "extensions.vector(768)",
         "metadata": "jsonb"
     })
 

apps/docs/content/guides/ai/examples/nextjs-vector-search.mdx

@@ -130,7 +130,7 @@ Let's prepare the database schema. We can use the "OpenAI Vector Search" quickst
       page_id bigint not null references public.nods_page on delete cascade,
       content text,
       token_count int,
-      embedding vector(1536),
+      embedding extensions.vector(1536),
       slug text,
       heading text
     );
@@ -156,7 +156,7 @@ Let's prepare the database schema. We can use the "OpenAI Vector Search" quickst
     ```sql
     -- Create embedding similarity search functions
     create or replace function match_page_sections(
-        embedding vector(1536),
+        embedding extensions.vector(1536),
         match_threshold float,
         match_count int,
         min_content_length int

apps/docs/content/guides/ai/hybrid-search.mdx

@@ -53,7 +53,7 @@ create table documents (
   id bigint primary key generated always as identity,
   content text,
   fts tsvector generated always as (to_tsvector('english', content)) stored,
-  embedding vector(512)
+  embedding extensions.vector(512)
 );
 ```
 
@@ -83,7 +83,7 @@ Finally we'll create our `hybrid_search` function:
 ```sql
 create or replace function hybrid_search(
   query_text text,
-  query_embedding vector(512),
+  query_embedding extensions.vector(512),
   match_count int,
   full_text_weight float = 1,
   semantic_weight float = 1,
@@ -158,7 +158,7 @@ select
 from
   hybrid_search(
     'Italian recipes with tomato sauce', -- user query
-    '[...]'::vector(512), -- embedding generated from user query
+    '[...]'::extensions.vector(512), -- embedding generated from user query
     10
   );
 ```

apps/docs/content/guides/ai/langchain.mdx

@@ -36,12 +36,12 @@ create table documents (
   id bigserial primary key,
   content text, -- corresponds to Document.pageContent
   metadata jsonb, -- corresponds to Document.metadata
-  embedding vector(1536) -- 1536 works for OpenAI embeddings, change if needed
+  embedding extensions.vector(1536) -- 1536 works for OpenAI embeddings, change if needed
 );
 
 -- Create a function to search for documents
 create function match_documents (
-  query_embedding vector(1536),
+  query_embedding extensions.vector(1536),
   match_count int default null,
   filter jsonb DEFAULT '{}'
 ) returns table (

apps/docs/content/guides/ai/rag-with-permissions.mdx

@@ -29,7 +29,7 @@ create table document_sections (
   id bigint primary key generated always as identity,
   document_id bigint not null references documents (id),
   content text not null,
-  embedding vector (384)
+  embedding extensions.vector (384)
 );
 ```
 
@@ -176,7 +176,7 @@ create table document_sections (
   id bigint primary key generated always as identity,
   document_id bigint not null,
   content text not null,
-  embedding vector (384)
+  embedding extensions.vector (384)
 );
 ```
 

apps/docs/content/guides/ai/semantic-search.mdx

@@ -48,15 +48,15 @@ To implement semantic search in Postgres we use `pgvector` - an extension that a
    create table documents (
      id bigint primary key generated always as identity,
      content text,
-     embedding vector(512)
+     embedding extensions.vector(512)
    );
    ```
 
    Or if you have an existing table, you can add a vector column like so:
 
    ```sql
    alter table documents
-   add column embedding vector(512);
+   add column embedding extensions.vector(512);
    ```
 
    In this example, we create a column named `embedding` which uses the newly enabled `vector` data type. The size of the vector (as indicated in parentheses) represents the number of dimensions in the embedding. Here we use 512, but adjust this to match the number of dimensions produced by your embedding model.
@@ -80,7 +80,7 @@ The easiest way to perform semantic search in Postgres is by creating a function
 ```sql
 -- Match documents using cosine distance (<=>)
 create or replace function match_documents (
-  query_embedding vector(512),
+  query_embedding extensions.vector(512),
   match_threshold float,
   match_count int
 )
@@ -108,7 +108,7 @@ You'll notice we are using the cosine distance (`<=>`) operator in our query. Co
 ```sql
 -- Match documents using negative inner product (<#>)
 create or replace function match_documents (
-  query_embedding vector(512),
+  query_embedding extensions.vector(512),
   match_threshold float,
   match_count int
 )
@@ -142,7 +142,7 @@ You can also call this method directly from SQL:
 ```sql
 select *
 from match_documents(
-  '[...]'::vector(512), -- pass the query embedding
+  '[...]'::extensions.vector(512), -- pass the query embedding
   0.78, -- chose an appropriate threshold for your data
   10 -- choose the number of matches
 );

apps/docs/content/guides/ai/structured-unstructured.mdx

@@ -13,7 +13,7 @@ Most vector stores treat metadata associated with embeddings like NoSQL, unstruc
 ```sql
 create table docs (
   id uuid primary key,
-  embedding vector(3),
+  embedding extensions.vector(3),
   content text,
   url text
 );
@@ -31,7 +31,7 @@ Notice that we've associated two pieces of metadata, `content` and `url`, with t
 ```sql
 create table docs (
   id uuid primary key,
-  embedding vector(3),
+  embedding extensions.vector(3),
   meta jsonb
 );
 
@@ -84,7 +84,7 @@ The structured metadata style is recommended when the fields being tracked are k
 ```sql
 create table docs (
   id uuid primary key,
-  embedding vector(3),
+  embedding extensions.vector(3),
   content text,
   url string,
   meta jsonb

apps/docs/content/guides/ai/vector-columns.mdx

@@ -55,7 +55,7 @@ create table documents (
   id serial primary key,
   title text not null,
   body text not null,
-  embedding vector(384)
+  embedding extensions.vector(384)
 );
 ```
 
@@ -113,7 +113,7 @@ Supabase client libraries like `supabase-js` connect to your Postgres instance v
 
 ```sql
 create or replace function match_documents (
-  query_embedding vector(384),
+  query_embedding extensions.vector(384),
   match_threshold float,
   match_count int
 )

apps/docs/content/guides/database/extensions/http.mdx

@@ -94,7 +94,7 @@ A successful call to a web URL from the `http` extension returns a record with t
 select
   "status", "content"::jsonb
 from
-  http_get('https://jsonplaceholder.typicode.com/todos/1');
+  extensions.http_get('https://jsonplaceholder.typicode.com/todos/1');
 ```
 
 ### Simple `POST` example
@@ -103,7 +103,7 @@ from
 select
   "status", "content"::jsonb
 from
-  http_post(
+  extensions.http_post(
     'https://jsonplaceholder.typicode.com/posts',
     '{ "title": "foo", "body": "bar", "userId": 1 }',
     'application/json'