Extend the SSL_set_bio() tests

The SSL_set_bio() tests only did standalone testing without being in the
context of an actual connection. We extend this to do additional tests
following a successful or failed connection attempt. This would have
caught the issue fixed in the previous commit.

Reviewed-by: Viktor Dukhovni <viktor@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/5966)