Save PSB to internal drive failed but no error dialog appears - leads to lost of my work

You did get a warning: scratch disk full. The fact that you later couldn't save is just an inevitable consequence of that. It's a side effect, so to speak.

Sorry to be blunt, I don't mean to be rude. It's just that this is a brick wall you can't get around, and you need to take this as a valuable lesson for the future. Photoshop can't operate without enough scratch disk space and that's basically all there is to it.

If you get the scratch disk full message, you may be able to save the situation by immediately deleting all history states (and close any other documents). But it may be too late. I wouldn't know; I have never seen that message (I have several TB available at all times).

And if for some reason you must work even knowing you really don't have enough space, set History States to 1. That means you can't go back, but the scratch file won't build up so quickly.

The file is now about 3,6 GB. And I do understand that 70GB is poor for managing big files.

But you miss the main issue I'm reporting. There is no problem in that the file was not saved BUT the saving process of the file seems from application user point of view as succesfully finished. If I get the error dialog with "Not enough space available on the disk" I would say fine, lets delete some stuff to save my work.

This is the issue. Saving process failed WITHOUT error dialog letting the user know about that? This happend in the early stage of PCs where no multitasking was ever belieavable.  

How large was the file? if the scrach disk was full there was no room to save the file.

Normally when you run out of disk space, Photoshop starts to cascade fail and crashes.

You should designate a secondary drive as your scratch disk or add more disk space to your internal drive.

Agree with @D Fosse 70 GB is nowhere near enough to run Photoshop without issues.

Not a bug. 70 GB free space is just nowhere near enough for working with big files! This isn't about the size of the file itself. The  scratch file contains all history states (each potentially as big as the file) for all open documents, plus overhead for moving all that data around. Anything big enough to need the PSB format will require at least 400 - 600 GB to be safe.

The real problem here is that Adobe don't emphasize the scratch disk enough in the official system requirements. This should be a big warning right at the top.