Location Manager service providing an asynchronous way of accessing the user current location.

LocationManager.swift

import Foundation
import CoreLocation

class LocationManager: NSObject, CLLocationManagerDelegate {
    
    //MARK: Object to Access Location Services
    private let locationManager = CLLocationManager()
    
    //MARK: Set up the Location Manager Delegate
    override init() {
        super.init()
        locationManager.delegate = self
    }
    
    //MARK: Request Authorization to access the User Location
    func checkAuthorization() {
        switch locationManager.authorizationStatus {
        case .notDetermined:
            locationManager.requestWhenInUseAuthorization()
        default:
            return
        }
    }
    
    //MARK: Continuation Object for the User Location
    private var continuation: CheckedContinuation<CLLocation, Error>?
    
    // Error messages associated with the location manager
    enum LocationManagerError: String, Error {
        case replaceContinuation = "Continuation replaced."
        case locationNotFound = "No location found."
    }
    
    //MARK: Async Request the Current Location
    var currentLocation: CLLocation {
        get async throws {
            // Check if there is a continuation being worked on
            if self.continuation != nil {
                // If so, resumes it throwing an error
                self.continuation?.resume(throwing: LocationManagerError.replaceContinuation)
                // And deletes it, so a new one can be created
                self.continuation = nil
            }
            
            return try await withCheckedThrowingContinuation { continuation in
                // 1. Set up the continuation object
                self.continuation = continuation
                // 2. Triggers the update of the current location
                locationManager.requestLocation()
            }
        }
    }
    
    func locationManager(_ manager: CLLocationManager, didUpdateLocations locations: [CLLocation]) {
        // 4. If there is a location available
        if let lastLocation = locations.last {
            // 5. Resumes the continuation object with the user location as result
            continuation?.resume(returning: lastLocation)
            // Resets the continuation object
            continuation = nil
        } else {
            // If there is no location, resumes the continuation throwing and error to avoid a continuation leak
            continuation?.resume(throwing: LocationManagerError.locationNotFound)
        }
    }
    
    func locationManager(_ manager: CLLocationManager, didFailWithError error: Error) {
        // 6. If not possible to retrieve a location, resumes with an error
        continuation?.resume(throwing: error)
        // Resets the continuation object
        continuation = nil
    }
    
}

UserLocationMapView.swift

import SwiftUI
import MapKit

struct ContentView: View {
    // MARK: Instance of the location manager
    var locationManager = LocationManager()
    
    // MARK: Properties
    @State var location: CLLocation?
    
    // MARK: Position of the MapCamera
    @State private var position: MapCameraPosition = .automatic
    
    // MARK: Body
    var body: some View {
        VStack {
            Map(position: $position) {
                UserAnnotation()
            }
            .clipShape(RoundedRectangle(cornerRadius: 15))
            .shadow(radius: 5)
            
            Text(location?.description ?? "No location yet")
                .padding()
                .foregroundColor(.secondary)
            
            Button {
                Task { await self.updateLocation() }
            } label: {
                Text("Get Location")
            }
        }
        .padding()
        .background {
            Color.gray.opacity(0.4)
                .ignoresSafeArea()
        }
        .task {
            // 1. Check if the app is authorized to access the location services of the device
            locationManager.checkAuthorization()
        }
    }
    
    // MARK: Get the current user location if available
    func updateLocation() async {
        do {
            // 1. Get the current location from the location manager
            self.location = try await locationManager.currentLocation
            // 2. Update the camera position of the map to center around the user location
            self.updateMapPosition()
        } catch {
            print("Could not get user location: \(error.localizedDescription)")
        }
    }
    
    // MARK: Change the camera of the Map view
    func updateMapPosition() {
        if let location = self.location {
            let regionCenter = CLLocationCoordinate2D(
                latitude: location.coordinate.latitude,
                longitude: location.coordinate.longitude
            )
            let regionSpan = MKCoordinateSpan(latitudeDelta: 0.125, longitudeDelta: 0.125)
            
            self.position = .region(MKCoordinateRegion(center: regionCenter, span: regionSpan))
        }
    }
    
}

Solved! I've updated the location manager so a continuation is always resumed, in every code path. Thanks for the feedback!