Incorrect I-94, new passport, H1B transfer

[krishna-gopinath]

Ok, I think I may be confusing a lot of things here. My visa status changed from F1 -> H1B last October. I went to India this January, got the H1B visa stamped, renewed my Indian passport and returned on Feb 1. The H1B visa is on my old passport and my "port of entry" stamp (from Abu Dhabi) with the visa change is on my new passport.
I am currently in the process of switching jobs and the attorneys asked me for my latest I-94. Here's when things get tricky:

• I entered my new passport number and the website tells me that I have no records. Basically, no I-94 for my new passport,
• When I go to the travel history section, and type in the new passport number, it accurately shows that entered the US on Feb 1.
• When I enter my old passport number, the I-94 shows up. But it's old, because
  • it shows my visa status as F1
  • the "Most Recent Date of Entry" section shows up as Dec 2018

I read somewhere that when you enter the country with a new visa status & passport, the I-94 gets changed to that. But I'm not seeing that on my I-94. Is this a problem? Would this hurt my chances of this H1B transfer?