Does the Series X do this? If the Xbox One does, I've never seen it. The Switch tracks hours by multiples of 5.... Am I being dense, what am I missing?
They added it back in the Xbox One days and continued to capture the stats with the Series consoles. It's what powers the various MS reward quests for playing games and travelling X amount of distance etc.
Looks like back in 2014 there was at least one game in my list (Ground Zeros) not populating the time played stat but updating others such as "Longest Range Headshot" so not clear if this is something configurable by the games or the 'time played' stat collection was added later on. All the games I've played in the last couple of years that I've checked appear to be tracking all stats, including time played, accurately.
There's a couple of ways to get to the stats area but one of the quickest is to highlight a game -> menu button -> "go to official club" -> tab over to progress -> press down to access the stats area.
You can also access it from your profile or by viewing achievements.
You can see a leaderboard of where you stand amongst your friends for each individual stat on each game if that's of interest.
Interestingly for me, it appears to have captured my playtime on Resident Evil VII accurately. I used Quick Resume on that a lot which broke the in-game timer (it thinks I've played it for a very, very long time) but the stats page has an accurate reading of 13 hours and 59 minutes.
Not sure if this was the kind of thing you were looking for? As I said, I'm not familiar with the daily log you referenced.
Edit: Forgot to mention, you can also access the stats via the mobile app for some games. Just go into your profile, click a game in the achievement list and the stats will be available via a tab. As noted, not all games show their stats via the app, Outriders shows nothing for me in the app but on the console has a full listing.