In case anyone wonders, I went ahead an ordered this battery

https://www.amazon.com/gp/product/B07815961L/

mainly because the seller specified the thickness in Q&A: the original battery is 27mm thick, and this replacement is 29mm. The battery has arrived and I have replaced it about an hour ago. The additional 2mm thickness didn't allow to push the battery all the way down, but since the original battery was also taller, there was enough space to squeeze in this battery. The lower white cover fits a bit snugger than before, but I think it’s ok.

Now, the most important part: the battery works! When I disconnect the AC adapter, an orange light turns on (failure indication) but the gateway stays on. When arming, it says that gateway is experiencing power failure, but that's exactly what it should say. After plugging AC back the failure light goes off as expected. So far it looks good.

So, contrary to what Abode says, the battery in the Gateway is relatively easy to replace. It's a shame Abode itself would not provide the proper fitting part, but the replacement batteries available on amazon still can do the trick and you will not need to shell out $200 for a new Gateway.