docs: fix broken docs URLs and add API key comment to examples

Replace runcycles.github.io/docs and docs.runcycles.io with the correct
runcycles.io domain. Add inline comment to CYCLES_API_KEY placeholder
in examples/README.md.

https://claude.ai/code/session_01HftF1nebzvUzQy4y4zGJk6

Author: claude

README.md

@@ -46,14 +46,14 @@ def call_llm(prompt: str, tokens: int) -> str:
 result = call_llm("Hello", tokens=100)
 ```
 
-> **Need an API key?** API keys are created via the Cycles Admin Server (port 7979). See the [deployment guide](https://docs.runcycles.io/quickstart/deploying-the-full-cycles-stack#step-3-create-an-api-key) to create one, or run:
+> **Need an API key?** API keys are created via the Cycles Admin Server (port 7979). See the [deployment guide](https://runcycles.io/quickstart/deploying-the-full-cycles-stack#step-3-create-an-api-key) to create one, or run:
 > ```bash
 > curl -s -X POST http://localhost:7979/v1/admin/api-keys \
 >   -H "Content-Type: application/json" \
 >   -H "X-Admin-API-Key: admin-bootstrap-key" \
 >   -d '{"tenant_id":"acme-corp","name":"dev-key","permissions":["reservations:create","reservations:commit","reservations:release","reservations:extend","reservations:list","balances:read","decide","events:create"]}' | jq -r '.key_secret'
 > ```
-> The key (e.g. `cyc_live_abc123...`) is shown only once — save it immediately. For key rotation and lifecycle details, see [API Key Management](https://docs.runcycles.io/how-to/api-key-management-in-cycles).
+> The key (e.g. `cyc_live_abc123...`) is shown only once — save it immediately. For key rotation and lifecycle details, see [API Key Management](https://runcycles.io/how-to/api-key-management-in-cycles).
 
 ### Programmatic client
 
@@ -115,7 +115,7 @@ config = CyclesConfig.from_env()
 # Reads: CYCLES_BASE_URL, CYCLES_API_KEY, CYCLES_TENANT, etc.
 ```
 
-> **Need an API key?** See the [deployment guide](https://docs.runcycles.io/quickstart/deploying-the-full-cycles-stack#step-3-create-an-api-key) or [API Key Management](https://docs.runcycles.io/how-to/api-key-management-in-cycles).
+> **Need an API key?** See the [deployment guide](https://runcycles.io/quickstart/deploying-the-full-cycles-stack#step-3-create-an-api-key) or [API Key Management](https://runcycles.io/how-to/api-key-management-in-cycles).
 
 ### All options
 

examples/README.md

@@ -4,12 +4,12 @@ Runnable examples demonstrating how to integrate the `runcycles` client into rea
 
 ## Prerequisites
 
-1. A running Cycles server (see [Deploy the Full Stack](https://runcycles.github.io/docs/quickstart/deploying-the-full-cycles-stack))
+1. A running Cycles server (see [Deploy the Full Stack](https://runcycles.io/quickstart/deploying-the-full-cycles-stack))
 2. Set environment variables:
 
 ```bash
 export CYCLES_BASE_URL="http://localhost:7878"
-export CYCLES_API_KEY="your-api-key"
+export CYCLES_API_KEY="your-api-key"   # create via Admin Server — see link above
 export CYCLES_TENANT="acme"
 ```