I believe for the tire pressure stuff that much like the old TCU's and MyFord Mobile, with these H series TCU's it's only going to alert you if tire pressures are low but won't go into more detail. Supposedly, based on info on the F150 forums Sync Connect retrofit thread, the Hotspot equipped J/K TCU's will show individual tire pressures.
There IS a trick that someone made me aware of in the CyanLabs Discord where you can pull in more detailed info than what the app shows through the Ford website. Unfortunately with no data being populated on mine yet, this trick is also unavailable to me. But you may have better luck @David_Tucker4: OTA Update Status Hidden in the Ford Website | MachEforum - Ford Mustang Mach-E Forum, News, Owners, Discussions
I did notice the Oil Life icon pop up on mine as well. Still no data though just yet.