This app was mentioned in 10 comments, with an average of 2.00 upvotes
I have the Z Play and use Pacer as my pedometer. I like the clean UI, graphed information and it's lightweight and reliable enough for my purposes. That said, I think all phone based pedometers are inherently unreliable and best used as just general activity measures rather than anything else.
In the past I've used Pedometer and later a Xiaomi Mi Band, and the numbers I'm currently seeing with the Huawei Health app on my Mate SE are in the same ballpark so I'd guess it's fairly decent. But I have no idea how accurate pedometers are. This 2017 study of physical devices produced some not so great results, especially for the Fitbit. If hip-based pedometers are more accurate than those worn on the wrist, I wonder what that means for a device in a shirt pocket... Ah well, I usually fall 2/3rds short of my 10k step goal every day anyway. :P
Pacer. tried loads; stuck with this one: https://play.google.com/store/apps/details?id=cc.pacer.androidapp&referrer=utm_source%3Dmypacer.com%26utm_campaign%3DWebsite%2520Referrals
Not manually but I have Pacer app which counts my daily steps. Once I tried counting manually and found no difference.
Glad I could help!
The OPO is very very clean - it comes with a blank ROM if I recall correctly. Only the usual Google apps come on it stock. S Health sounds like something that comes preinstalled on Samsung phones - bloatware. Part OPO's philosophy was to cut that stuff out, because often it includes a lot of useless junk. Unfortunately this means that some of the better apps (if S Health was one of them) aren't available. You have to find an alternative to it on the Play store. I checked it out and it looks like S Health track steps, heartrate, etc. I think Google Fit does something similar, but I'm not very well affiliated with the fitness apps on the Play store (AKA I'm relatively lazy). I'm sure a bit of searching around will help you find what you need!
TL;DR No, there are almost no non-stock apps installed on the OPO.
EDIT - I did a search and someone is in the same boat as you - moving from GS4 to OPO, looking for a S Health replacement. I think they came to the conclusion that the Pacer Pedometer app was the best. Maybe try that?
EDIT 2 - Here is another thread that has the "Move" app recommended. I've seen this recommended as an S Health alternative a few times now. Try checking out Google Fit too. It's integrated with your Google account!
Edit 3 - Looks like people prefer to use MyFitnessPal as a calorie counter. Apparently it synergizes with Move. Not sure about Pacer or Google Fit though. This heartrate monitor was recommended too.