I'm unsure of the way you're injecting the BASE_URL, but perhaps this can read it? It works when passing in with --dart-define, and should also as args/toolArgs (unsure which) in the launch config.

const baseUrl = bool.hasEnvironment("BASE_URL")
    ? String.fromEnvironment("BASE_URL")
    : "https://example.dev.com";

Source: https://api.flutter.dev/flutter/dart-core/String/String.fromEnvironment.html