TL;DR. Explore Yosemite on foot.

I don't know Yellowstone, but the situation with Yosemite is a bit complicated. There are basically two congestion issues:

1. Congestion in the park itself. 2. Traffic.

Yosemite is huge, but the only places that are really built out are Yosemite Valley (where most people go) and Tuolomne Meadows (where a lot of climbers go). Most of Yosemite is backcountry and just accessible by foot. So what happens is that most people go to one of these two places (which, to be clear, really are spectacular) and then stay within a few km radius of the parking lot, hence the crowding. But once you get outside that, it's quite empty. I've done 50-odd mile loops in Yosemite and seen basically nobody [0].

As far as traffic goes, there are very few entrances to the park. If you're coming in from the bay area, you're probably coming in through the Tioga Road/Big Oak Flat entrance. As a result, even if you want to be in some part of the park where there are very few other people, you can end up having to wait in line to enter with the giant mobs of people who want to go to the Valley. The fix here is to enter super early or super late, when there basically is no line.

[0] https://educatedguesswork.org/posts/northern-yosemite/

Yeah I always come in Yosemite from the south. I can hike all day and see nobody.