Not just medical notifications being "late", also seeing with Watch faces. An Automation/Shortcut to change a Watch face runs on time but face does not change for a minute or two. And at times, this might cause some conflicts, out of order changes.
I have an Automation, "A", that runs to turn off my bedtime Focus at the same time each day. As part of that, a call is made to change the Watch face to my "daytime" face (I have a "when bedtime turns off" Automation that runs as a result of Automation "A" turning off the Focus and part of that is to switch the Watch face from bedtime face, should I be waking up from nap where I turned bedtime Focus on and/or waking up early and manually turned off the Focus).
Two minutes later, I have an Automation "B" that runs and as a part of that, a different Watch face is set, usually my workout face as I usually do cardio first thing in the morning on most days.
So, should see workout face when getting ready, but some days would see daytime. Verified everything running in proper order as I was writing log messages to a file each time my "Set Watch Face" Shortcut ran: would see "setting daytime", and two minutes later see "setting workout" in the log file, but there is the pesky daytime face showing.
(Was easily coded around as I'm setting a flag "IsBedtime" when my normal "bedtime" window starts, so, "if IsBedtime is true, don't set daytime face when bedtime Focus turns off")