Cloud Function for Proximity Matching and Push Notifications in Service App

I am developing a service marketplace app using FlutterFlow and require a specialized backend function. This project focuses solely on implementing a robust Cloud Function (Firebase or Supabase) to handle proximity-based service request matching, push notifications, and secure order acceptance.

The core logic for this function includes:
1.  **Proximity Matching**: Upon the creation of a new service order in the database, the function must identify registered users who meet the following criteria:
    *  They are qualified for the specific service category of the request.
    *  They are currently marked as "available" in their profile.
    *  They are located within a defined X km radius of the order's location, requiring efficient geospatial search capabilities.
2.  **Push Notifications**: Send targeted push notifications via Firebase Cloud Messaging (FCM) to all eligible users identified in the matching process.
3.  **Secure Order Acceptance**: Implement an atomic transaction mechanism to securely lock an order when a user accepts it. This system must prevent race conditions, ensuring that only one user can successfully accept an order at any given time. If multiple users attempt to accept simultaneously, only the first successful transaction should proceed, and others should receive an "already accepted" notification.
4.  **Radius Expansion Logic**: If no user accepts the service request within a specified timeframe (e.g., A few minutes), the system should automatically expand the search radius and re-attempt the matching and notification process.

Existing components:
*  All app screens, user interface flow, and design are complete in FlutterFlow.
*  The category structure for services is defined.
*  User registration and two distinct user profile types are already implemented.

Deliverables from the freelancer:
*  Development and thorough testing of the Cloud Function, encompassing geospatial matching, push notification integration, and the atomic transaction for order acceptance.
*  Provide concise guidance on how to integrate this function effectively with the existing FlutterFlow application.
*  This project is strictly for the technical backend function; no design work or additional app screens are required.

Preferred Technology Stack:
*  Backend Database: Firebase or Supabase (freelancer may suggest the most suitable/economical option).
*  Frontend App: FlutterFlow.

Proposal Requirement: I am seeking a fixed-budget proposal with an estimated deadline for this specific function. Please include a brief explanation (2-3 sentences) of your proposed solution for handling the "race condition" problem (multiple users attempting to accept the same request simultaneously) to demonstrate relevant experience.