Changes the `Read` and `Write` error handling
logic to return the original error while closing
the connection. We still skip calling `handleEOF`
if already closing the connection.
Fixes the flaky `TestCloseWhileWriting` and
`TestCloseWhileReading` tests.
Co-authored-by: Sebastiaan van Stijn <github@gone.nl>
Signed-off-by: Laura Brehm <laurabrehm@hey.com>