LosslessCut is great, but I've had issues with the final export like timing being off, having cut sequence etc. I think it is very particular about encoding/container.
Shotcut is my default video editor, if anyone's trying it on Linux please use their AppImage as it solved most of my headaches when I was using Flatpak version.
If it's lossless, it may change the cut position to enable lossless. If you want cut at an exact place, then all apps need to re-encode which will never be lossless.
For your particular requirement, you can't get lossless quality all the time by any software.