Move price badges to python nodes (#7816)

## Summary

Backend part: https://github.com/Comfy-Org/ComfyUI/pull/11582

- Move API node pricing definitions from hardcoded frontend functions to
backend-defined JSONata expressions
- Add `price_badge` field to node definition schema containing JSONata
expression and dependency declarations
- Implement async JSONata evaluation with signature-based caching for
efficient reactive updates
- Show one decimal in credit badges when meaningful (e.g., 1.5 credits
instead of 2 credits)

## Screenshots (if applicable)

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┆Issue is synchronized with this [Notion
page](https://www.notion.so/PR-7816-Move-price-badges-to-python-nodes-2da6d73d365081ec815ef61f7e3c65f7)
by [Unito](https://www.unito.io)

src/schemas/nodeDefSchema.ts

@@ -197,6 +197,50 @@ const zComfyOutputTypesSpec = z.array(
   z.union([zComfyNodeDataType, zComfyComboOutput])
 )
 
+/**
+ * Widget dependency with type information.
+ * Provides strong type enforcement for JSONata evaluation context.
+ */
+const zWidgetDependency = z.object({
+  name: z.string(),
+  type: z.string()
+})
+
+export type WidgetDependency = z.infer<typeof zWidgetDependency>
+
+/**
+ * Schema for price badge depends_on field.
+ * Specifies which widgets and inputs the pricing expression depends on.
+ * Widgets must be specified as objects with name and type.
+ */
+const zPriceBadgeDepends = z.object({
+  widgets: z.array(zWidgetDependency).optional().default([]),
+  inputs: z.array(z.string()).optional().default([]),
+  /**
+   * Autogrow input group names to track.
+   * For each group, the count of connected inputs will be available in the
+   * JSONata context as `g.<groupName>`.
+   * Example: `input_groups: ["reference_videos"]` makes `g.reference_videos`
+   * available with the count of connected inputs like `reference_videos.character1`, etc.
+   */
+  input_groups: z.array(z.string()).optional().default([])
+})
+
+/**
+ * Schema for price badge definition.
+ * Used to calculate and display pricing information for API nodes.
+ * The `expr` field contains a JSONata expression that returns a PricingResult.
+ */
+const zPriceBadge = z.object({
+  engine: z.literal('jsonata').optional().default('jsonata'),
+  depends_on: zPriceBadgeDepends
+    .optional()
+    .default({ widgets: [], inputs: [], input_groups: [] }),
+  expr: z.string()
+})
+
+export type PriceBadge = z.infer<typeof zPriceBadge>
+
 export const zComfyNodeDef = z.object({
   input: zComfyInputsSpec.optional(),
   output: zComfyOutputTypesSpec.optional(),
@@ -224,7 +268,13 @@ export const zComfyNodeDef = z.object({
    * Used to ensure consistent widget ordering regardless of JSON serialization.
    * Keys are 'required', 'optional', etc., values are arrays of input names.
    */
-  input_order: z.record(z.array(z.string())).optional()
+  input_order: z.record(z.array(z.string())).optional(),
+  /**
+   * Price badge definition for API nodes.
+   * Contains a JSONata expression to calculate pricing based on widget values
+   * and input connectivity.
+   */
+  price_badge: zPriceBadge.optional()
 })
 
 export const zAutogrowOptions = z.object({