Engine Cooling Circuit Logic?

I think someone here may be able to explain what I am observing. Sorta cold right now, 20s and 30s DegF. Upon cold start, I notice the coolant gauge creep from COLD to 1/4 in a “short” duration ~3 min of driving and stays there for “some time”. Warm/Hot air comes from the HVAC

Then after a “noticeably longer duration” the needle moves from 1/4 --> 1/2 (middle). At this point OBD shows ~91DegC

Is this normal or part of the “diverting” cooling circuit these 5.2’s have? Pump and t-stat was replaced 58k ago so possibly stuck? I would assume a cel if the tstat was stuck

I have just always noticed on most cars a linear coolant gauge warm up not a “2-step”