The proxy server servicing makeImageRequest() cannot resolve domain name

It looks like you're right. It might not be a DNS issue.
I wrote a verification code. It loads three images. Each link opens correctly in the browser.
The first link is needed to verify that my code is working correctly.
The other two are examples of failed image retrieval directly from the site and through my proxy.
In the proxy logs, I see the request and successful transfer of the image to the Garmin server. Interestingly, the error codes for retrieval directly and through the proxy are different.

import Toybox.Communications;
import Toybox.Lang;
import Toybox.System;
import Toybox.Media;
import Toybox.Time;
import Toybox.Application;

class AbooksSyncDelegate extends Communications.SyncDelegate {
  var links = null;
  var index = null;

  function initialize() {
    SyncDelegate.initialize();
    links = [];
    // A good link for checking the correctness of the code
    links.add(
      "https://habrastorage.org/r/w780/getpro/habr/upload_files/713/a92/5a8/713a925a8f41db887179e66cb822f201.jpg"
    );
    // Direct link to the image. Doesn't work, although accessible from the browser.
    links.add(
      "https://akniga.org/uploads/media/topic/2025/11/28/23/preview/252ddce3185c910fdbb1_400x.webp"
    );
    // The previous link is accessed through the my proxy. Doesn't work, although accessible from the browser.
    // In the proxy logs, I see that the image was successfully sent to the Garmin server.
    links.add(
      "https://fv.n-drive.cf/audiobookshelf/cover?url=https://akniga.org/uploads/media/topic/2025/11/28/23/preview/252ddce3185c910fdbb1_400x.webp"
    );
  }

  function onStartSync() {
    index = 0;
    startLoadingCovers();
  }

  function startLoadingCovers() {
    if (index < links.size()) {
      var url = links[index];
      System.println("start: " + url);
      var options = {
        :maxWidth => 100,
        :maxHeight => 100,
        :dithering => Communications.IMAGE_DITHERING_FLOYD_STEINBERG,
        :packingFormat => Communications.PACKING_FORMAT_JPG,
      };

      Communications.makeImageRequest(
        url,
        {},
        options,
        self.method(:onWebResponse)
      );
    }
  }

  function onWebResponse(code, data) {
    System.println("code: " + code);
    System.println("data: " + data);

    index += 1;
    startLoadingCovers();
  }

  function isSyncNeeded() as Boolean {
    return true;
  }

  function onStopSync() as Void {
    Communications.cancelAllRequests();
    Communications.notifySyncComplete(null);
  }
}

console:

start: https://habrastorage.org/r/w780/getpro/habr/upload_files/713/a92/5a8/713a925a8f41db887179e66cb822f201.jpg
code: 200
data: Obj: 218
start: https://akniga.org/uploads/media/topic/2025/11/28/23/preview/252ddce3185c910fdbb1_400x.webp
code: 404
data: null
start: https://fv.n-drive.cf/audiobookshelf/cover?url=https://akniga.org/uploads/media/topic/2025/11/28/23/preview/252ddce3185c910fdbb1_400x.webp
code: 400
data: null

I explained this in the previous thread. The same resource is accessible or unavailable depending on the domain name you access it through.
They fixed the .cf zone, but it looks like others remain.

How do you know the problem is with the domain name?