I spent several hours chatting to an advisor at apple who was in discussion with engineers as I actually suspected it was my tattoos from articles read long ago. I was informed that pervious series didn't work at all. However, like you, the series 5 was working with heart rate etc but the not always on feature was not as it kept turning the screen off and locking the watch. So had they fixed something or was the sensors better, but not perfect?
Well, I was informed that Apple have worked on the sensors and they are better, however depending on the amount of ink coverage and even ink types, this is a very abstract and hard to pin down scenario, and wether it works accurately or works consistently various considerably.
So. after discussions I was directed to go to the Apple watch App on my iPhone and go to the passcode setting. From there I was instructed to have the passcode on, but turn wrist detection off. Now the always on works perfect and the watch functions 85% as normal... with the exception that apps like Apple pay won't work in this state. However, a work around is if you want to use it, you swipe the face down and click the manual lock icon, then Apple pay should work as you have fully locked the watch. After, if you turn the lock icon off from the swipe down screen on the watch, always on works again. The watch also still detects when you put it on to charge and then locks it also.
Apple support did say that the software is continually being worked on, so who knows in future whether the issues will entirely be ironed out as it is a mix of software and the sensors on your series 5.
For me personally. Thats how I use it rather than putting it on the wrong wrist. Yeah, you lose that added layer of security, but as you can log in on your phone with Find Me and locate, block or wipe the watch if you lose it or even worse case scenario got robbed, as the passcode is still active. Obviously, all this needs to connected to a iphone with a cellular data plan.
This isn't a perfect setup, but this is what I learnt from my chats with Apple, so I thought I would pass it on, from one tattooed apple user to another!! hope it helps.