REGR: Assigning label with registered EA dtype raises
- [x] closes #38386
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Previous behavior in `io.parsers` depended on `is_bool_dtype("boolean")` erroneously raising `AttributeError`.

Test currently iterates over the names:

> ['category', 'interval', 'boolean', 'Float32', 'Float64', 'Int8', 'Int16', 'Int32', 'Int64', 'UInt8', 'UInt16', 'UInt32', 'UInt64', 'string']

It skips any EA where the name is a property; I don't see a good way to iterate over these in the test.

I only added a note about `is_bool_dtype` in the whatsnew as the `DataFrame.__setitem__` issue does not occur on 1.1.x. It didn't seem appropriate for any section besides other.
thanks @rhshadrach  @meeseeksdev backport 1.2.x