Observing this behaviour, It appeared to me that perhaps the male was the first to abandon the nest and since the female relies on him for raising the kids later on she had to abandon it too. So after the female left the nest for the fourth time that morning, she never came back into the birdbox.
In the following days I have seen the couple feeding in the trees near the birdbox and the female then went to the birdbox and peeked through the entrance (but didn’t enter). I have not seen the male showing any interest in the birdbox anymore, whereas before he was always checking it. Around the same period I still saw the female begging the male for food (and getting it) so the couple had definitely not broken up.
I haven’t seen the couple recently though I occasionally see the male singing in the trees. But since there are so many leaves on the trees now it has become very difficult to keep track of the birds.
So what actions did I take to prevent further cat attacks? I got a good tip from somebody on the internet. She successfully prevented cats from climbing a tree by mounting a surgical dog collar around the tree trunk. Because this could be done without disturbing the nest I mounted this immediately (the largest size I could get, obviously):
Anti-cat shield will hopefully prevent cats from reaching the birdbox
Should a cat still be able to reach the birdbox, it will be difficult for him to sit on the roof and try to reach through the entrance like I saw him doing on that fateful day.
Unfortunately, none of this changes the fate of the current nest but at least I’ll be better prepared for a new nest hopefully next year.