With Redux and Context, you might have test setup code always populate the store with reasonable defaults for the 20 different data dependencies. Then, a typical test might update a few things in the store with test-specific values, render <Nav /> without the need to specify any props, and then perform interactions, inspect the results, etc. There's more going on behind the scenes, but it's also easier to get started because you don't need to figure out 20 props.
(There are many, many ways to think about testing here, though, and this is just one approach.)
If you want to test the connected component, it's still good to separate them as you won't test the same things (correct props are passed down, rather than UI renders)
As one (admittedly extreme) example, a while back I hit an issue where a refactor caused a very simple crash: just load the app, click a particular button, and it immediately crashes. All relevant components, actions, stores etc had extensive unit tests, but there was no test to make sure that the component dispatched an action that was compatible with what the store wants. I wrote an integration test for it, "load the app and click this button, and assert the intended effect", and it ended up being about 5 lines. It exercised the same code paths as the hundreds of lines of unit tests, and gives me much more confidence in the overall correctness of the system.
I'd like to move to a page-based testing, where I mount the entire page and interact with it, asserting what's going on visually and in the store
The costs of deep prop trees 1) kills many performance benefits offered by a good react/redux setup 2) makes it hard to build off of the state (much like a monolithic codebase) because it can be harder to find if something is already there or not.
1. unit testing on the smallest bits (Redux actions/reducers make unit testing them SUPER easy)
2. do e2e with something like Cypress.
Anything in between can be helpful but I found it can be too tedious, or difficult to do and ultimately, unit/e2e catches most things