I don't know Wasabi well enough to comment, but GTR uses Azure because of its unique(?) ability to do cloud-initiated fetches, versus "download to my computer, upload to the S3 endpoint" that every other cloud storage API uses. All of the words you haven't read yet were about trickery to exfiltrate the signed Takeout URLs so that Azure's blob storage could fetch them (along with some Cloudflare Worker trickery to work around some kind of bugs in Azure)

So, I guess the TL;DR (heh, quite literally in this case) is that if Wasabi allows you to download something like an Ubuntu ISO to Wasabi storage by giving it the ISO URL from your phone, it'll likely work for you. Otherwise, you're back in the VPS setup TFA was seeking to avoid