Upgrade to RN v0.66

[gnprice]

The next round after #5230. (Which at present we haven't done yet, but this gives us a place to leave information about this version.) Blog post here:
https://reactnative.dev/blog/2021/10/01/version-066

There's no mention of anything incompatible, so (like v0.65, #5230) this might be an easier upgrade than usual. More-detailed changelog:
https://github.com/facebook/react-native/blob/main/CHANGELOG.md#v0660

[gnprice]

One item in the blog post that stands out as potentially helpful:

Handle taps on child views outside parent boundaries on Android​

Thanks to @hsource for adding interaction support for children rendered outside of parent view boundaries via overflow: visible. This is a common use-case and aligns React Native on Android more closely with web standards.

Find more details on the pull request.

I seem to recall us running into that recently, in #5130.