Feature request: Add Kakao OAuth2 provider support

[mrbonk97]

Prerequisites

• I have written a descriptive issue title
• I have searched existing issues to ensure the feature has not already been requested

🚀 Feature Proposal

Description

@fastify/oauth2 does not include support for Kakao OAuth2.

Kakao Login is one of the most widely used OAuth providers in South Korea.

• KakaoTalk has over 100M+ downloads on Google Play
• Kakao accounts are commonly used as a primary login method for consumer services

Proposal

• Add a built-in kakao provider following existing provider patterns

Willingness to contribute

I am willing to implement this feature and submit a PR if maintainers agree with the approach.

Motivation

No response

Example

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