Cleanup the s_time command.

Various code-cleanups.
Use SSL_CTX_set_mode(ctx, SSL_MODE_AUTO_RETRY) insead of handling
SSL_ERROR_WANT_READ everywhere.
Turn off the linger option on connected sockets to avoid failure.
Add BIO_set_conn_mode(conn, BIO_SOCK_NODELAY) to improve thruput.

Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/3952)