feat: add ListMysqlDatabases endpoint

[VoLKyyyOG]

Create new endpoint for use by metanexus.
This lists all mysql databases.

ref: https://linear.app/squareup/issue/DFNS-445/create-schemabot-endpoint-listmysqldatabases

[Copilot]

Pull request overview

Adds a new API endpoint for listing configured MySQL databases from SchemaBot’s server configuration.

Changes:

• Defines response types for MySQL database inventory.
• Registers and implements GET /api/mysql/databases with optional environment filtering.
• Adds handler tests and updates API README route documentation.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated no comments.

Show a summary per file

File	Description
pkg/apitypes/apitypes.go	Adds response structs for MySQL database inventory.
pkg/api/service.go	Registers the new MySQL database listing route.
pkg/api/README.md	Documents the new route and handler file.
pkg/api/mysql_handlers.go	Implements the MySQL database inventory handler and filtering logic.
pkg/api/mysql_handlers_test.go	Adds tests for listing, filtering, and empty configuration behavior.

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[aparajon]

Triage review of this draft, which has been open a while — sharing an honest assessment of where it stands relative to the current codebase:

1. The API shape conflicts with the engine-agnostic surface rule — pkg/apitypes and the route are MySQL-specific (/api/mysql/databases, MysqlDatabaseResponse), but the API layer is required to stay engine-agnostic; a database listing should be a generic GET /api/databases registry view that works for all engine types, with engine-specific data in metadata.

2. Correctness: the Deployment field is populated with the database name — deployment is per-environment configuration, so consumers would receive fabricated routing metadata.

3. Staleness — the branch is ~174 commits behind main and predates the per-environment deployments map, which the response type can't represent. There's also an exported handler wrapper that's a pure delegation (the repo avoids those).

4. PR description — the body references an internal service and an internal issue tracker link; per repo policy those need to be removed from public PR descriptions regardless of outcome.

Given the schema-pull/onboarding primitives now landing (#313), the recommendation is to close this and re-approach the need as an engine-agnostic database listing on top of that work. Happy to discuss if there's a use case the generic shape wouldn't cover.

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🤖 This review was generated by Claude Code (claude-fable-5) with maintainer approval.