I really have no idea but I have a hard time believing it’s an issue with digitakt’s USB unless the audio out’s physical connection is somehow shorting the USB connection? A simple test that you can perform is NOT with OB but just using DT as the USB audio source, create a single track USB audio recording directly from DT with your audio out cable still plugged in. So that means selecting DT as your audio source (not via OB) and recording all 8 DT tracks or however many on your test track at the master output down to 1 DAW track.
If you can successfully complete a recording over USB while NOT using OB that means there is nothing physically wrong with DT and it’s unlikely the problem is a setting (that means it could be a bug and a setting may affect it, but it’s unlikely a setting is causing it). If this same setup was working for you previously and there isn’t some change to your physical arrangement or settings that you aren’t telling us about, I’d encourage you to (on the DT) try taking it out of overbridge mode and then re-enable it, also change the setting for usb / midi / usb + midi (so whichever it’s in now, switch it and then switch back to the one that was working previously).
If you’re plugged into a USB hub, try bypassing the hub and go straight into one of your computer’s USB 2.0 ports, if you’ve already done that then tell us if there’s anything else physically in between the DT and the computer.
Really, if you want someone to help you, you’ll really need to state your computer (pc or mac) and operating system, the version of OS would probably help especially if it’s a mac. Also, any kind of changes leading up to the issue would probably be key in figuring out what happened, even if it seems like something trivial or inconsequential.
It is indeed a very strange problem but rarely do these things happen without cause, I for one have never heard of this happening so I don’t know how much I can help and this is still bottom level troubleshooting just one beyond changing cables like you already did. I’m just hoping with some more info on the table, someone else will have a better idea and might be able to aid you in resolving your issue. It could be an overbridge problem, it could be an ableton problem? It seems like it’s a DT problem but right now there’s no way to know. I do, however, agree that it shouldn’t be doing this.