Fixed #13559 -- Made current site available through context manager.

[FarhanAliRaza]

13559

ticket-13559

Branch description

Provide a concise overview of the issue or rationale behind the proposed changes.

Checklist

• This PR targets the main branch.
• The commit message is written in past tense, mentions the ticket number, and ends with a period.
• I have checked the "Has patch" ticket flag in the Trac system.
• I have added or updated relevant tests.
• I have added or updated relevant docs, including release notes if applicable.
• I have attached screenshots in both light and dark modes for any UI changes.

[github-actions]

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