I saw your most recent post in a separate topic/thread. Posting in only one topic/thread will make it easier for others to follow (I think you can merge your threads - ask a forum moderator if you need help).
Until you can get some more info (like from kdump as you mentioned), support is likely your best option.
FWIW, I have a core ultra series 1 125H running ubuntu 24.04 lts (kernel 7.0.0-14-generic, X11, bios updated to 3.07) for a little more than a year now. I’ve had one crash (with some similar symptoms you describe - processes locking up followed by a crash over a 1-2 min period) that I believe was related to my samsung 990 pro (1TB) nvme drive. In my case, there was some pretty obvious signs the device could not read/write to the nvme over this period. I updated the nvme firmware and have not had a crash since (about 6 months ago).
So while your working with support and trying to get some additional error messages, you can see if you can update your nvme firmware (assuming an update is available and you haven’t already tried this).
Another intel 125H/fedora user had hardware issues with the intel igpu (link here). This apparently was a hardware issue and needed a main board replacement. You can have a look through your logs for similar errors.
Seems like a hardware issue to me, but you’ll need more info to narrow it down. Good luck.