Fix: Connectors: AI provider API keys are re-validated on every settings update (/wp/v2/settings), causing needless provider calls and key resets

[hbhalodia]

Trac ticket: https://core.trac.wordpress.org/ticket/65867

Description

• Fixed the issue related to settings check for API key for all connectors, even if the request does not changes or have connector key.
• This leads to unnecessary calls to provider to check for API key on every settings save via wp/v2/settings.

Use of AI Tools

• Yes, Claude Code, Opus 5.
• Used for drafting the ticket mentioned.
• Used for adding the unit test for the changes mentioned. Tested locally and reviewed tests by me.

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[github-actions]

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