Hi Martijn,
I suspect that reason that you don't see the "send report" option under Troubleshooting is that you don't have email configured on your iPhone. If you are able to configure email (some corporate iPhone's will not allow email to be configured) you can easily set up your iCloud email on the device long enough to send the diagnostics. It would be very helpful to get the diagnostics as it is hard to troubleshoot the problem without this information.
There are cases where the OSTC data gets corrupted on the device itself so that the requested dive(s) report one size in the dive list but the profile data returned is truncated (this appears to happen when the OSTC battery is very low during a dive). I would expect that your Linux download would also fail in this case though.
Dive Log will sometimes successfully download your OSTC but will get an error while disconnecting from the OSTC. This gets reported as an error, but the download actually worked. In this case you would see that the "Import" button shows dives available to import even though you got the error (you can still tap on the button and import the dives. One case where this would not show any dives is if the most recent dive on the OSTC was older than the most recent dive in your logbook (this might be the case if you synced your dives from another location). In that case you can trey tapping on the "All dives" option instead often reference dive option *before* you start your download. This might be worth a try anyways.
Dive Log (and Subsurface) download your most recent dives first in all cases. So if there is a corrupted and it is the most recent dive then the download will terminate almost immediately. That said, the error message you are getting suggests that the issue is with the Bluetooth connection as a download error due to a corrupted dive should give a different error (although it is possible that you got both the real error and the "disconnect" error so only the disconnect errors showing).
Because this happens with both Dive Log and Subsurface, It would be worth verifying the battery state in your OSTC (Bluetooth might disconnect due to a low battery). It would also be worth restarting your iPhone (
https://support.apple.com/en-us/HT201559). However, since you have been having this difficulty for some time I suspect that you have have tried it with various battery levels and after restarts before. It would really be best if you can send me your diagnostics log.
Cheers,
Greg