This is a real pain to be honest, and I do not know why this happens.
The other metadata does
And all the image capture metadata?
So why not the keywords?
Check out this image, which is featured in my latest article on Improve Photography.
This is the Lightroom Classic image showing the Title, Capton, Copyright and filename.
But when I go to the keyword tab, just above the info tab in the bottom right hand corner, this is what I get in Lightroom Mobile.
Here is a screenshot of the same image in Lightroom Classic 7.3 taken from my PC.
So what is going on? Time to ask Adobe.