Implements unified model routing

Migrates the AMP module to a new unified routing system, replacing the fallback handler with a router-based approach.

This change introduces a `ModelRoutingWrapper` that handles model extraction, routing decisions, and proxying based on provider availability and model mappings.
It provides a more flexible and maintainable routing mechanism by centralizing routing logic.

The changes include:
- Introducing new `routing` package with core routing logic.
- Creating characterization tests to capture existing behavior.
- Implementing model extraction and rewriting.
- Updating AMP module routes to utilize the new routing wrapper.
- Deprecating `FallbackHandler` in favor of the new `ModelRoutingWrapper`.

internal/routing/testutil/fake_proxy.go

@@ -0,0 +1,83 @@
+package testutil
+
+import (
+	"io"
+	"net/http"
+	"net/http/httptest"
+)
+
+// CloseNotifierRecorder wraps httptest.ResponseRecorder with CloseNotify support.
+// This is needed because ReverseProxy requires http.CloseNotifier.
+type CloseNotifierRecorder struct {
+	*httptest.ResponseRecorder
+	closeChan chan bool
+}
+
+// NewCloseNotifierRecorder creates a ResponseRecorder that implements CloseNotifier.
+func NewCloseNotifierRecorder() *CloseNotifierRecorder {
+	return &CloseNotifierRecorder{
+		ResponseRecorder: httptest.NewRecorder(),
+		closeChan:        make(chan bool, 1),
+	}
+}
+
+// CloseNotify implements http.CloseNotifier.
+func (c *CloseNotifierRecorder) CloseNotify() <-chan bool {
+	return c.closeChan
+}
+
+// FakeProxyRecorder records proxy invocations for testing.
+type FakeProxyRecorder struct {
+	Called         bool
+	CallCount      int
+	RequestBody    []byte
+	RequestHeaders http.Header
+	ResponseStatus int
+	ResponseBody   []byte
+}
+
+// NewFakeProxyRecorder creates a new fake proxy recorder.
+func NewFakeProxyRecorder() *FakeProxyRecorder {
+	return &FakeProxyRecorder{
+		ResponseStatus: http.StatusOK,
+		ResponseBody:   []byte(`{"status":"proxied"}`),
+	}
+}
+
+// ServeHTTP implements http.Handler to act as a reverse proxy.
+func (f *FakeProxyRecorder) ServeHTTP(w http.ResponseWriter, r *http.Request) {
+	f.Called = true
+	f.CallCount++
+	f.RequestHeaders = r.Header.Clone()
+
+	body, err := io.ReadAll(r.Body)
+	if err == nil {
+		f.RequestBody = body
+	}
+
+	w.WriteHeader(f.ResponseStatus)
+	w.Write(f.ResponseBody)
+}
+
+// GetCallCount returns the number of times the proxy was called.
+func (f *FakeProxyRecorder) GetCallCount() int {
+	return f.CallCount
+}
+
+// Reset clears the recorder state.
+func (f *FakeProxyRecorder) Reset() {
+	f.Called = false
+	f.CallCount = 0
+	f.RequestBody = nil
+	f.RequestHeaders = nil
+}
+
+// ToHandler returns the recorder as an http.Handler for use with httptest.
+func (f *FakeProxyRecorder) ToHandler() http.Handler {
+	return http.HandlerFunc(f.ServeHTTP)
+}
+
+// CreateTestServer creates an httptest server with this fake proxy.
+func (f *FakeProxyRecorder) CreateTestServer() *httptest.Server {
+	return httptest.NewServer(f.ToHandler())
+}