docs: Improve GitHub Copilot connection docs tone and structure

aider/website/docs/llms/github.md

@@ -3,44 +3,56 @@ parent: Connecting to LLMs
 nav_order: 510
 ---
 
-# GitHub Copilot models
+# GitHub Copilot compatible API
 
-Aider can talk to the GitHub Copilot LLMs because Copilot exposes an **OpenAI-compatible** REST
-API at `https://api.githubcopilot.com`.
+Aider can connect to GitHub Copilot’s LLMs because Copilot exposes a standard **OpenAI-style**
+endpoint at:
 
-The only trick is getting an OAuth access token that has permission to call the Copilot
-endpoint.  
-The easiest, **official** way is to sign in to Copilot from any JetBrains IDE
-(Goland, PyCharm, etc).  
-After you sign in, a file appears at:
+```
+https://api.githubcopilot.com
+```
+
+First, install aider:
+
+{% include install.md %}
+
+---
+
+## Configure your environment
+
+```bash
+# macOS/Linux
+export OPENAI_API_BASE=https://api.githubcopilot.com
+export OPENAI_API_KEY=<oauth_token>
+
+# Windows (PowerShell)
+setx OPENAI_API_BASE https://api.githubcopilot.com
+setx OPENAI_API_KEY  <oauth_token>
+# …restart the shell after setx commands
+```
+
+---
+
+### Where do I get the token?
+The easiest path is to sign in to Copilot from any JetBrains IDE (PyCharm, GoLand, etc).
+After you authenticate a file appears:
 
 ```
 ~/.config/github-copilot/apps.json
 ```
 
-Inside you will find an `oauth_token` value – copy that string, **it is your API key**.
+Copy the `oauth_token` value – that string is your `OPENAI_API_KEY`.
+
+*Note:* tokens created by the Neovim **copilot.lua** plugin (old `hosts.json`) sometimes lack the
+needed scopes. If you see “access to this endpoint is forbidden”, regenerate the token with a
+JetBrains IDE or the VS Code Copilot extension.
 
 ---
 
-## Configure the environment
-
-```bash
-# macOS/Linux
-export OPENAI_API_BASE=https://api.githubcopilot.com
-export OPENAI_API_KEY=<oauth_token from apps.json>
-
-# Windows (PowerShell)
-setx OPENAI_API_BASE https://api.githubcopilot.com
-setx OPENAI_API_KEY  <oauth_token>
-# …restart the shell so the variables are picked up
-```
-
----
-
-## Pick a model
+## Discover available models
 
 Copilot hosts many models (OpenAI, Anthropic, Google, etc).  
-You can discover the list that your subscription allows with:
+List the models your subscription allows with:
 
 ```bash
 curl -s https://api.githubcopilot.com/models \
@@ -49,8 +61,7 @@ curl -s https://api.githubcopilot.com/models \
   -H "Copilot-Integration-Id: vscode-chat" | jq -r '.data[].id'
 ```
 
-The returned IDs are used exactly like OpenAI models, but **prefixed with `openai/`** when you
-pass them to aider:
+Each returned ID can be used with aider by **prefixing it with `openai/`**:
 
 ```bash
 aider --model openai/gpt-4o
@@ -58,7 +69,21 @@ aider --model openai/gpt-4o
 aider --model openai/claude-3.7-sonnet-thought
 ```
 
-You can also store this in `~/.aider.conf.yml`:
+---
+
+## Quick start
+
+```bash
+# change into your project
+cd /to/your/project
+
+# talk to Copilot
+aider --model openai/gpt-4o
+```
+
+---
+
+## Optional config file (`~/.aider.conf.yml`)
 
 ```yaml
 openai-api-base: https://api.githubcopilot.com
@@ -70,13 +95,11 @@ show-model-warnings: false
 
 ---
 
-## Notes & FAQ
+## FAQ
 
-* Copilot billing is handled entirely by GitHub.  Calls made through aider count against your
-  Copilot subscription, even though aider will still print estimated costs.
-* Tokens created by **Neovim copilot.lua** or older `hosts.json` files sometimes lack the
-  required scopes. If you get `access to this endpoint is forbidden`, regenerate the token via a
-  JetBrains IDE or VS Code Copilot extension.
-* The Copilot terms of service allow third-party “agents” that access the LLM endpoint.  Aider
-  merely follows the documented API and **does not scrape the web UI**.
+* Calls made through aider are billed through your Copilot subscription  
+  (aider will still print *estimated* costs).
+* The Copilot docs explicitly allow third-party “agents” that hit this API – aider is playing by
+  the rules.
+* Aider talks directly to the REST endpoint—no web-UI scraping or browser automation.