Based on the images, I think the real question is: does the Fitness app track steps when Watch battery dies? And I don't know.
Fitness app will
track steps if you don't have an Apple Watch. But, guessing here, if one does have a Watch, Fitness app will not use phone's steps. Or probably more accurately, won't record via the sensors. Bug or "working as designed by Apple". Fitness is not listed in "Allow to Read" for steps data in Health. So, seems like an either/or situation with Fitness app.
Looking at my data for today, I did put my Watch on the charger when I woke up. Walked a bit around the house to make coffee etc. Steps in Health are a bit higher than in Fitness, and pretty much aligns with the raw data in Health (most of the extra steps were recorded as phone, with the remaining extra couple of steps from phone appear to overlap with Watch recording again).
ADD: and looking at the day I mentioned earlier when I did not have my Watch on, it too is pretty much in sync re lesser amount of steps Fitness is showing (quick and dirty math of steps that are from phone only during the time without Watch was in the ball park re differences).
So, app of record should probably be Health and not Fitness. And yes, if the whole closing of rings is a big deal to someone, not ideal for Fitness to not track steps when Watch not in use.