Looks like I solved this issue. I didn't do anything though.
For me, this was not fulfilled although my sim improved writing skill level up to 10.
But anyway, I sent him to work and set the work status as 'work hard'.
I heard the good music sound and checked he got promoted although the promotion task was not recognized.
Now after the promotion,the promotion task is fully recognized.
If it doesn't work, then try to send your sim to work from other lot.
In my case, he was about to attend the graduation ceremony.
Suddenly he started to move while waiting the graduation ceremony in Britechester Uni lot.
I had another sim for graduation ceremony, so I sent him to work straightaway from Uni lot.
I feel like it might be connected with this bug that the sim loses their prep tasks after moving to other lots for acting sim like this.
After coming back home from Graduation ceremony..
It shows as they are not completed. It's just my personal opinion. =)
I'm sorry to show this another issue but I'm not asking for fixing this bug.
I just wanted to show these to explain my opinion.
How about trying to move to another lot and see the task is still not recognized?
In my case, this bug is rather a display error in the career panel. My sim in the style influencer career skilled up the Photography skill to 3, the career panel still showed it at level 2. But my sim went to work and he got promoted despite in the career panel, the Photography skill was still shown as if it is at level 2.
