So looking at this, just to clarify, did you actually upgrade the Supervisor, or not yet? It can be done via the drop-down menu when you are on a device’s details page in balenaCloud.
No, I did not. Thanks for pointing this out!
So I just did the upgrade (following this post, I ran $ update-resin-supervisor -t v12.5.10 in a host shell on my device since I wanted to stay in local mode). So far, things are looking very good! The first balena push is working without problems and curl localhost:48484 hasn’t shown any hanging or timeout, either!
My colleague just did the same and it seems to be working for him, too! Looks like it was indeed the supervisor then!
Once again, thank you for your help!
Question: Are images for the Jetson devices released manually by your team or is there an automatic build process involved? In any case: Could you update the Xavier image with the updated supervisor? 
(In fact, now that I’m thinking about it: Would a supervisor upgrade via balenaCloud even work if the supervisor’s API is unreachable?)