We have this same issue going on right now (March 2024).  I had our IT clear the cache/cookies per the linked instructions in this thread.  That process did not resolve the issue.  I have contacted QB support.

In the past I was able to delete the newly entered project, then once I recreate it, the new project showed up on the employees tsheets.  However, this issue happens too often and the delete/recreate method is not a sustainable solution.

Here's hoping support has a fix.