Unless the developer vladyslav.volovyk returns to development, we are all out in the cold. He was last seen a year ago, just as I bought a paid mode for both chrome (still works, but with all of the problems above) and Edge chromium (stopped working with errors when Edge updated to match the latest version of chromium).
Same issue here trying to download tabs saved on my other computer, which used to work well. I can see all of the backups from both this and my laptop, but cannot view any of the cloud saved ones any longer - not even the ones saved from this computer!
Customer support service by UserEcho
The saddest thing is that shortly after my OP, an update to Edge broke tabs outliner paid for status, and since then despite having paid, I can only use the free version in Edge. Emails sent were unanswered. Other users reckon that because it was chromium, tough. I was lucky to have it work at all. I've got the paid for Chrome version which works great, even if it keeps forgetting I'm a paid up user.
As the developer seems to have abandoned the project (again, shortly after I had paid} , and it is not open source, there is no hope of any improvement from what we've got now. Unless of course someone re-engineers it, which is far far beyond my abilities.