Yes, it was downloaded. Here is my console output:

%
========================== CocoaPods output BEGIN ===========================
Analyzing dependencies
Adding spec repo `trunk` with CDN `https://cdn.cocoapods.org/`
Downloading dependencies
Installing AppsFlyerFramework (6.5.4)
Installing Firebase (8.13.0)
Installing FirebaseABTesting (8.15.0)
Installing FirebaseAnalytics (8.13.0)
Installing FirebaseCore (8.13.0)
Installing FirebaseCoreDiagnostics (8.15.0)
Installing FirebaseCrashlytics (8.13.0)
Installing FirebaseInstallations (8.15.0)
Installing FirebaseMessaging (8.13.0)
Installing FirebaseRemoteConfig (8.13.0)
Installing Google-Mobile-Ads-SDK (9.6.0)
Installing GoogleAppMeasurement (8.13.0)
Installing GoogleDataTransport (9.1.4)
Installing GoogleUserMessagingPlatform (2.0.0)
Installing GoogleUtilities (7.7.0)
Installing PromisesObjC (2.1.1)
Installing nanopb (2.30908.0)
Generating Pods project
Integrating client project
%

Ok, I will do it some later.

I sent it just now. Sorry, took some time to do it.

I updated my iOS SDK version to 15.5.

In xcode project that I sent you, I forgot to disable Appodeal plugin, and there is another problem with it, which I wanted to deal with later, but it seems, I must describe it now.
At start of CocoaPods, Appodeal repo is cloning:

%
Cloning spec repo `appodeal-cocoapods` from `https://github.com/appodeal/CocoaPods.git`
%

It's ok, but then cocoa finds a lot of multiple specifications, like this:

%
[!] Found multiple specifications for `APDAppLovinAdapter (3.0.0.1)`:
- /Users/cocoapods/.cocoapods/repos/trunk/Specs/a/c/2/APDAppLovinAdapter/3.0.0.1/APDAppLovinAdapter.podspec.json
- /Users/cocoapods/.cocoapods/repos/appodeal-cocoapods/APDAppLovinAdapter/3.0.0.1/APDAppLovinAdapter.podspec.json
%

I'm not specialist in CocoaPods and I don't understand, why it happens.

Also, there is another little problem, with Firebase Remote Config - cocoa can't find compatible version, and it is too related to the Appodeal plugin, because APDFirebaseAdapter is one of Appodeal's adapter:

%
[!] CocoaPods could not find compatible versions for pod "Firebase/RemoteConfig":
  In Podfile:
    APDFirebaseAdapter (= 3.0.0.1) was resolved to 3.0.0.1, which depends on
      Firebase/RemoteConfig (~> 8.15.0)

    Firebase/RemoteConfig (= 8.13.0)
%

I tested it on macOS. CocoaPod's behaviour is same. Unfortunately, it's realy a CocoaPods problem. I will try to talk with Appodeal's support, maybe they know, how to fix it.

I found a temporary solution - I removed Firebase dependencies from pod file, which had different version than Appodeal's plugin dependencies. It's not final, I will need to synchronize versions of Firebase in project and firebase in cocoa for Appodeal. Anyway, Cocoa finished successfully, and builder started building project, but then builder showed this:

%
 + [arm64] Compiling Pods/CriteoPublisherSdk/CriteoPublisherSdk/Sources/SKAdNetwork/SKAdNetworkInfo.swift...
error: your project contains code written in the Swift language, but the Swift compiler hasn't been ported to Windows yet.
Possible workarounds:
 - If this source file is part of a third-party dependency, look for an Objective-C/C++ only version of that dependency and use it instead.
 - If this source file is part of your project itself, rewrite it in C, C++, Objective-C or Objective-C++.
%

It seemed to me, builder already has some undocumented tools to build swift code, but they are not integrated in final build script. So, how to use them to build .swift files or it is not possible right now?=)

It would be interesting for me solve this problem and do some experiments, but I will not make any promises that I will be able to do this in the near future for the same reason of lack of time and because I have always been far from subtleties of Apple technology.