supabase / supabase / 21653352384

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Introduce connection details in home (#42400)

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<img width="887" height="573" alt="image"
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This introduces database url under project title which reveals summary
to connection details that then reveals full connect dialog if needed.
Increases exposure to connection info which we know some people struggle
to find.

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **New Features**
* Added a project connection hover card showing Data API (project URL,
publishable key) and Database connection string with copyable, read-only
fields, loading/permission states, and a "Get connected" action to open
connection setup.

* **UI Improvements**
* Integrated the connection hover card into the top section; reorganized
title and badge layout for clearer hierarchy and adjacent controls.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

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Co-authored-by: Joshen Lim <joshenlimek@gmail.com>

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