docs(supabase): provide info for connecting to Supabase postgres

docs/docs/core/initialization.mdx

@@ -1,20 +1,24 @@
 ---
 title: Initialization
-description: Initialize the CocoIndex library
+description: Initialize and set environment for CocoIndex library
 ---
 
 import Tabs from '@theme/Tabs';
 import TabItem from '@theme/TabItem';
 
 # Initialize the CocoIndex Library
 
-Before everything starts, the `cocoindex` library needs to be initialized with settings.
-There're two options to do this:
+Before everything starts, the CocoIndex library needs to be initialized with settings.
+We'll talk about the code skeleton to initialize the library in your code, and the way to provide settings for CocoIndex.
 
-*   Using packaged main function. It's easier to start with.
+## Initialize the library
+
+There're two options to initialize in your code:
+
+*   Use packaged main function. It's easier to start with.
 *   Explicit initialization. It's more flexible.
 
-## Using Packaged Main
+### Packaged Main
 
 The easiest way is to use a packaged main function:
 
@@ -45,33 +49,13 @@ This takes care of the following effects:
     See [CocoIndex CLI](/docs/core/cli) for more details.
 3.  Otherwise, it will run the main function.
 
-### Environment Variables
-
-The following environment variables are supported:
+See [Environment Variables](#environment-variables) for supported environment variables.
 
-*   `COCOINDEX_DATABASE_URL` (required): The URL of the Postgres database to use as the internal storage, e.g. `postgres://cocoindex:cocoindex@localhost/cocoindex`
-*   `COCOINDEX_DATABASE_USER` (optional): The username for the Postgres database. If not provided, username will come from `COCOINDEX_DATABASE_URL`.
-*   `COCOINDEX_DATABASE_PASSWORD` (optional): The password for the Postgres database. If not provided, password will come from `COCOINDEX_DATABASE_URL`.
 
-## Explicit Initialization
+### Explicit Initialization
 
 Alternatively, for flexibility, you can also explicitly initialize the library by the `init()` function:
 
-### Settings
-
-It takes a `Settings` object as argument, which is a dataclass that contains the following fields:
-
-*   `database` (type: `DatabaseConnectionSpec`, required): The connection to the Postgres database.
-
-#### DatabaseConnectionSpec
-
-`DatabaseConnectionSpec` has the following fields:
-*   `url` (type: `str`, required): The URL of the Postgres database to use as the internal storage, e.g. `postgres://cocoindex:cocoindex@localhost/cocoindex`.
-*   `user` (type: `str`, optional): The username for the Postgres database. If not provided, username will come from `url`.
-*   `password` (type: `str`, optional): The password for the Postgres database. If not provided, password will come from `url`.
-
-### Example
-
 <Tabs>
 <TabItem value="python" label="Python" default>
 
@@ -93,4 +77,45 @@ if __name__ == "__main__":
 ```
 
 </TabItem>
-</Tabs>
+</Tabs>
+
+## Settings
+
+`cocoindex.Settings` is used to configure the CocoIndex library.  It's a dataclass that contains the following fields:
+
+*   `database` (type: `DatabaseConnectionSpec`, required): The connection to the Postgres database.
+
+### DatabaseConnectionSpec
+
+`DatabaseConnectionSpec` configures the connection to a database. Only Postgres is supported for now. It has the following fields:
+
+*   `url` (type: `str`, required): The URL of the Postgres database to use as the internal storage, e.g. `postgres://cocoindex:cocoindex@localhost/cocoindex`.
+*   `user` (type: `str`, optional): The username for the Postgres database. If not provided, username will come from `url`.
+*   `password` (type: `str`, optional): The password for the Postgres database. If not provided, password will come from `url`.
+
+:::tip
+
+Please be careful that all values in `url` needs to be url-encoded if they contain special characters.
+For this reason, prefer to use the separated `user` and `password` fields for username and password.
+
+:::
+
+:::info
+
+If you use the Postgres database hosted by [Supabase](https://supabase.com/), please click **Connect** on your project dashboard and find the following URL:
+
+*    If you're on a IPv6 network, use the URL under **Direct connection**. You can visit [IPv6 test](https://test-ipv6.com/) to see if you have IPv6 Internet connection.
+*    Otherwise, use the URL under **Session pooler**.
+
+:::
+
+## Environment Variables
+
+When you use the packaged main function, settings will be loaded from environment variables.
+Each setting field has a corresponding environment variable:
+
+| environment variable | corresponding field in `Settings` | required? |
+|---------------------|-------------------|----------|
+| `COCOINDEX_DATABASE_URL` | `database.url` | Yes |
+| `COCOINDEX_DATABASE_USER` | `database.user` | No |
+| `COCOINDEX_DATABASE_PASSWORD` | `database.password` | No |