Also, is it different for HU and nit ring?

For me, it's about 6.3% of all the hands I'm dealt, but I'm a weird passive nit. For some aggro players even if they are loose pre-flop it might be nearer 5%. (EDIT: I just checked with a buddy who plays looser and more aggro than me, and his number was 5.9%).

You can find your own number in HEM by running the advanced filter "hero saw river = true" and then divide the number of hands that show up by however many you've been dealt in total.

If you want to know what proportion of hands that saw a flop also saw a river (or saw a showdown), you'd have to run some other filters.
The main idea, however, is that not many hands that you're dealt see a river. If you play heads up, then the number is much greater, because you VPIP so much more often.

I mean the amount of all hands that reach the river, not just the amount of times an individual player (or Hero) reaches river

Oh, in that case, the quickest rough-and-ready counting method I can think of is to switch off all filters, list all hand histories with 20 per page, and then literally count how many had a full runout.
e.g.


Which shows 5 out of 20 hands in that mini-sample featured a river card.
I counted up the river cards in 100 hands, and it was only 22. That's playing 6-max micro zoom. In splashier games there would be more players seeing flops, turns and rivers, so you'd have to check your own population if that's what you're interested in. (Note that in zoom games, it's only about 50% of hands that even see a flop).
I'm not entirely sure if full ring would have higher or lower numbers. More players at the table might mean more flops are seen multiway, but everyone plays so tight that it possibly means that about the same number of rivers are seen as in 6-max.

Stacksize is a key factor here.

depends on the bet sizing used and the board texture, but lets say board texture was irrelevant, and the best sizing used on 3 streets was 2/3 pot. your felting range should be 21.6%. (by theory, if you use MDF)