Well, I also have this problem. There is no solution yet. I share my experience.
Previously: Kingston 2000 2 TB SSD worked on macOS for a year without any problems (and on ventura, and even on sonoma 14.1 for a while), and I also have a 2 TB Trascend HDD. My device - Macbook Pro 16 2021 1 TB. All these external disks were formatted after purchase in the format exFAT (to be available on both Mac and Windows).
A week ago, my SSD Kingston just started falling off, and my MacBook stopped recognizing it. I tried connecting it every now and then, either through a different cable from the HDD drive or through an adapter, but it was unstable—that is, it worked once and then it didn't work again.
1) At first, I thought the problem was with the storage device itself, but on Android, it connected quickly, and the files were transferred perfectly, without any delays. I mean, it works on Android.
2) Windows - I connected a ssd, it is recognized, but gives an error - and windows cannot fix it (as others wrote here that they managed to fix it this way - it didn't work for me) - that is, when connected, I had to choose "continue without checking for errors" and the folders open, but you can't copy them to Windows - it gives an error that the files are damaged. In this case, any file, even a video, even a small text document.
Therefore, it was not possible to extract the data using Windows. It doesn't work correctly (I think it's because of the disk format and MacOS was providing emergency assistance to the disk, so there are no permissions). I remind you that everything worked on the android.
3) MACOS - I have updated to sonoma 14.4.1 - and it doesn't work. The SSD blinks but is not recognized. And now my HDD disk takes a long time to connect - from 5-7 minutes until the Macbook recognizes it (before it was a minute, always!).
I restarted the system from safe boot mode via text support, and it also doesn't see the disk, but after restarting in normal mode, it recognized the disk once. In this way, I managed to copy the files to my disk. But the Finder started to freeze. And yes, after restarting, nothing works again. I repeated the event through this boot, then a normal reboot - and again the ssd started for one time. After disconnecting and reconnecting, it is no longer recognized. Emergency assistance is not provided - it also freezes, and the disk utility sometimes loads, sometimes not. In general, it doesn't work!
4) I tried to connect this SSD to my friend's MacBook, which has an old version of MACOS (9th or something), and it doesn't recognize it either.
....
So I don't know what kind of trouble it is, but looking at the stories of others, I'm sad that after spending a lot of money on equipment and disks, I can't work and it's not fixed by updating the system... Moreover, it happened suddenly and not even after the update, but until then it had been working for a year without complaints.