I'm not sure I understand. I don't see anything in either =DATE(...) function that would return time information as well. Your description claims that you are getting time information for the 2 Jan date, but not for the 3 Jan date. I cannot replicate that result based on what you wrote.

I would expect a formula that returns both date and time in this fashion would look something like =DATE(2022,1,2)+TIME(6,24,33) to return 2 Jan 2022 at 6:24:33 AM.

A sample file showing what you currently have might help us understand better.