Is it possible to make Apple Watch Series 5 measure heart rate (pulse), passively, all the time?
Apple Watch 4 does this for me and has since day one. 

Tap show all data at the bottom of health App on your phone to see your samples of data. 



I don’t think you can change the default sampling rate, but I’m seeing samples every few minutes all day and all night. At 12 to 13 samples an hour it’s hard to see what you’re going to get by doubling the data. 

During a workout session the sample rate is even higher so you can get some very large datasets if you have long workouts.