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/types.go

@@ -0,0 +1,62 @@
+package routing
+
+// RouteType represents the type of routing decision made for a request.
+type RouteType string
+
+const (
+	// RouteTypeLocalProvider indicates the request is handled by a local OAuth provider (free).
+	RouteTypeLocalProvider RouteType = "LOCAL_PROVIDER"
+	// RouteTypeModelMapping indicates the request was remapped to another available model (free).
+	RouteTypeModelMapping RouteType = "MODEL_MAPPING"
+	// RouteTypeAmpCredits indicates the request is forwarded to ampcode.com (uses Amp credits).
+	RouteTypeAmpCredits RouteType = "AMP_CREDITS"
+	// RouteTypeNoProvider indicates no provider or fallback available.
+	RouteTypeNoProvider RouteType = "NO_PROVIDER"
+)
+
+// RoutingRequest contains the information needed to make a routing decision.
+type RoutingRequest struct {
+	// RequestedModel is the model name from the incoming request.
+	RequestedModel string
+	// PreferLocalProvider indicates whether to prefer local providers over mappings.
+	// When true, check local providers first before applying model mappings.
+	PreferLocalProvider bool
+	// ForceModelMapping indicates whether to force model mapping even if local provider exists.
+	// When true, apply model mappings first and skip local provider checks.
+	ForceModelMapping bool
+}
+
+// RoutingDecision contains the result of a routing decision.
+type RoutingDecision struct {
+	// RouteType indicates the type of routing decision.
+	RouteType RouteType
+	// ResolvedModel is the final model name after any mappings.
+	ResolvedModel string
+	// ProviderName is the name of the selected provider (if any).
+	ProviderName string
+	// FallbackModels is a list of alternative models to try if the primary fails.
+	FallbackModels []string
+	// ShouldProxy indicates whether the request should be proxied to ampcode.com.
+	ShouldProxy bool
+}
+
+// NewRoutingDecision creates a new RoutingDecision with the given parameters.
+func NewRoutingDecision(routeType RouteType, resolvedModel, providerName string, fallbackModels []string, shouldProxy bool) *RoutingDecision {
+	return &RoutingDecision{
+		RouteType:      routeType,
+		ResolvedModel:  resolvedModel,
+		ProviderName:   providerName,
+		FallbackModels: fallbackModels,
+		ShouldProxy:    shouldProxy,
+	}
+}
+
+// IsLocal returns true if the decision routes to a local provider.
+func (d *RoutingDecision) IsLocal() bool {
+	return d.RouteType == RouteTypeLocalProvider || d.RouteType == RouteTypeModelMapping
+}
+
+// HasFallbacks returns true if there are fallback models available.
+func (d *RoutingDecision) HasFallbacks() bool {
+	return len(d.FallbackModels) > 0
+}