api: Use Huma to generate swagger docs and parse JSON automatically (#262)

## Motivation and Context

Currently there's a lot of unsafe manual JSON unmarshalling/marshalling,
and we have to manually keep the openapi schema in sync.

This PR migrates the API to
[Huma](https://github.com/danielgtaylor/huma), which appears like a
popular, well-maintained way to build APIs in Golang. I'm not a Golang
expert, but seemed highly recommended by Reddit + Claude and has a
decent star count. It provides automatic openapi spec generation and
docs hosting, JSON parsing, as well as the ability to add auth
middlewares etc.

## How Has This Been Tested?

Running locally, and poking at the endpoints

## Breaking Changes

Docs are served at `/docs` rather than `/v0/swagger/index.html` now

## Types of changes
<!-- What types of changes does your code introduce? Put an `x` in all
the boxes that apply: -->
- [ ] Bug fix (non-breaking change which fixes an issue)
- [x] New feature (non-breaking change which adds functionality)
- [x] Breaking change (fix or feature that would cause existing
functionality to change)
- [x] Documentation update

## Checklist
<!-- Go over all the following points, and put an `x` in all the boxes
that apply. -->
- [x] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [x] My code follows the repository's style guidelines
- [x] New and existing tests pass locally
- [x] I have added appropriate error handling
- [x] I have added or updated documentation as needed

## Additional context
<!-- Add any other context, implementation notes, or design decisions
-->

internal/api/router/v0.go

@@ -2,26 +2,19 @@
 package router
 
 import (
-	"net/http"
-
+	"github.com/danielgtaylor/huma/v2"
 	v0 "github.com/modelcontextprotocol/registry/internal/api/handlers/v0"
 	"github.com/modelcontextprotocol/registry/internal/auth"
 	"github.com/modelcontextprotocol/registry/internal/config"
 	"github.com/modelcontextprotocol/registry/internal/service"
 )
 
-// RegisterV0Routes registers all v0 API routes to the provided router
 func RegisterV0Routes(
-	mux *http.ServeMux, cfg *config.Config, registry service.RegistryService, authService auth.Service,
+	api huma.API, cfg *config.Config, registry service.RegistryService, authService auth.Service,
 ) {
-	// Register v0 endpoints
-	mux.HandleFunc("/v0/health", v0.HealthHandler(cfg))
-	mux.HandleFunc("/v0/servers", v0.ServersHandler(registry))
-	mux.HandleFunc("/v0/servers/{id}", v0.ServersDetailHandler(registry))
-	mux.HandleFunc("/v0/ping", v0.PingHandler(cfg))
-	mux.HandleFunc("/v0/publish", v0.PublishHandler(registry, authService))
-
-	// Register Swagger UI routes
-	mux.HandleFunc("/v0/swagger/", v0.SwaggerHandler())
-	mux.HandleFunc("/v0/swagger/doc.json", v0.SwaggerJSONHandler())
+	v0.RegisterHealthEndpoint(api, cfg)
+	v0.RegisterPingEndpoint(api)
+	v0.RegisterServersEndpoints(api, registry)
+	// v0.RegisterAuthEndpoints(api, authService)
+	v0.RegisterPublishEndpoint(api, registry, authService)
 }