Why is my flutter app not handling Spotify's API authorization after signing in?

I’m making a flutter app using Spotify’s API. I have a basic homepage that uses a button to launch a browser to login to Spotify. Here is my backend code:

import 'dart:convert';
import 'package:http/http.dart' as http;
import 'package:flutter/material.dart';
import 'package:url_launcher/url_launcher.dart';
import 'package:uni_links/uni_links.dart';

class SpotifyAuth with ChangeNotifier {
  final String CLIENT_ID = "My client ID";
  final String ClIENT_SECRET = "My client secret";
  final String REDIRECT_URI = "http://localhost:8000/callback";
  final String SCOPE = 'user-read-private user-read-email';
  // var state = 'your-state';
  late String _accessToken;
  late String _refreshToken;

  Uri createAuthenticationUri(){
    var query = [
      'response_type=code',
      'client_id=$CLIENT_ID',
      'scope=${Uri.encodeComponent(SCOPE)}',
      'redirect_uri=${Uri.encodeComponent(REDIRECT_URI)}',
    ];

    var queryString = query.join('&');
    var url = 'https://accounts.spotify.com/authorize?' + queryString;
    var parsedUrl = Uri.parse(url);
    return parsedUrl;
  }

  Future<void> launchInBrowser() async {
    if (!await launchUrl(
      createAuthenticationUri(),
      mode: LaunchMode.externalApplication,
    )){
      throw Exception('Could not launch Url');
    }
  }

  Future<void> launchAuth() async {
    await launchInBrowser();
    await initUniLinks();
  }

  Future<void> getAccessToken(String code) async {
    var body = {
      "grant_type": "authorization_code",
      "code": code,
      "redirect_uri": REDIRECT_URI,
      "client_id": CLIENT_ID,
      "client_secret": ClIENT_SECRET
    };
    // Create a request header with the required information
    var header = {
      "Content-Type": "application/x-www-form-urlencoded",
      "Authorization":
          "Basic ${base64Encode(utf8.encode("$CLIENT_ID:$ClIENT_SECRET>"))}"
    };
    // Send the request to the Spotify token endpoint
    var response = await http.post(
        Uri.parse("https://accounts.spotify.com/api/token"),
        body: body,
        headers: header);

    // Check if the request was successful
    if (response.statusCode == 200) {
      // Parse the JSON response
      var data = json.decode(response.body);
      // Get the access token from the response
      String accessToken = data["access_token"];

      // Store the access token for future use
      // ...
      _accessToken = accessToken;
    } else {
      print("Error");
    }
  }

  Future<void> initUniLinks() async {
    // Get the latest initial link
    String? initialLink = await getInitialLink();

    // Check if the link contains a Spotify authorization code
    if (initialLink != null && initialLink.contains("code=")) {
      // Extract the code from the link
      String code = initialLink.split("code=")[1];

      // Use the code to get an access token from Spotify
      getAccessToken(code);
    }
    else{
      print("Nothing");
    }
  }
}

My redirect URI is set in the spotify dashboard.

My app widget calls luanchAuth();
and then it should wait for the authentication code with initUniLinks() but it seems like initUniLinks() executes immediately without waiting for the authentication. When I authenticate in Spotify, it throws a generic "can’t connect to localhost" error page but the url includes the auth code that I need.

Not sure what I’m doing wrong here. Admittedly I’m new to Oauth and app-api-connections in general but I thought this would work.