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/server.go

@@ -6,6 +6,7 @@ import (
 	"net/http"
 	"time"
 
+	"github.com/danielgtaylor/huma/v2"
 	"github.com/modelcontextprotocol/registry/internal/api/router"
 	"github.com/modelcontextprotocol/registry/internal/auth"
 	"github.com/modelcontextprotocol/registry/internal/config"
@@ -17,20 +18,21 @@ type Server struct {
 	config      *config.Config
 	registry    service.RegistryService
 	authService auth.Service
-	router      *http.ServeMux
+	humaAPI     huma.API
 	server      *http.Server
 }
 
 // NewServer creates a new HTTP server
 func NewServer(cfg *config.Config, registryService service.RegistryService, authService auth.Service) *Server {
-	// Create router with all API versions registered
-	mux := router.New(cfg, registryService, authService)
+	// Create HTTP mux and Huma API
+	mux := http.NewServeMux()
+	api := router.NewHumaAPI(cfg, registryService, authService, mux)
 
 	server := &Server{
 		config:      cfg,
 		registry:    registryService,
 		authService: authService,
-		router:      mux,
+		humaAPI:     api,
 		server: &http.Server{
 			Addr:              cfg.ServerAddress,
 			Handler:           mux,