docs: fix background task context example

[marko1olo]

Closes #8.

Summary:

• Updates the background task context example to declare the ctx parameter it uses.
• Fixes the nearby console.log typos in the inline and background task examples.

Checks:

• npm run build
• git diff --check HEAD~1 HEAD

AI assistance disclosure:

• OpenAI Codex assisted with this change; the commit includes Co-authored-by: OpenAI Codex <codex@openai.com>.

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