OpenSSL: Fix re-handshake, error handling and re-enable rest of OpenSSL tests

I didn't touch the racy one. All other tests succeed for me

[ruff@dei glib-networking]$ G_TEST_BUILDDIR='/home/ruff/co/glib-networking/_build/tls/tests' G_TEST_SRCDIR='/home/ruff/co/glib-networking/tls/tests' GIO_MODULE_DIR='/home/ruff/co/glib-networking/_build/tls/openssl' /home/ruff/co/glib-networking/_build/tls/tests/connection-openssl 2>&1 | egrep -v 'GLib-(GIO-DEBUG|Net-Message)'
# random seed: R02Sb3f4c07f93b21d9ff079cd840eb3f013
1..38
# Start of tls tests
# Start of openssl tests
# Start of connection tests
ok 1 /tls/openssl/connection/basic
ok 2 /tls/openssl/connection/verified
ok 3 /tls/openssl/connection/verified-chain
ok 4 /tls/openssl/connection/verified-chain-with-redundant-root-cert
ok 5 /tls/openssl/connection/verified-chain-with-duplicate-server-cert
ok 6 /tls/openssl/connection/verified-unordered-chain
ok 7 /tls/openssl/connection/verified-chain-with-alternative-ca-cert
ok 8 /tls/openssl/connection/invalid-chain-with-alternative-ca-cert
ok 9 /tls/openssl/connection/client-auth
ok 10 /tls/openssl/connection/client-auth-rehandshake
ok 11 /tls/openssl/connection/client-auth-failure
# Bug Reference: http://bugzilla.gnome.org/793712
ok 12 /tls/openssl/connection/client-auth-fail-missing-client-private-key
ok 13 /tls/openssl/connection/client-auth-request-cert
ok 14 /tls/openssl/connection/client-auth-request-fail
ok 15 /tls/openssl/connection/client-auth-request-none
ok 16 /tls/openssl/connection/no-database
ok 17 /tls/openssl/connection/failed
ok 18 /tls/openssl/connection/socket-client
ok 19 /tls/openssl/connection/socket-client-failed
ok 20 /tls/openssl/connection/read-time-out-then-write
ok 21 /tls/openssl/connection/simultaneous-async
ok 22 /tls/openssl/connection/simultaneous-sync
ok 23 /tls/openssl/connection/simultaneous-async-rehandshake
ok 24 /tls/openssl/connection/simultaneous-sync-rehandshake
ok 25 /tls/openssl/connection/close-immediately
ok 26 /tls/openssl/connection/unclean-close-by-server
# Bug Reference: http://bugzilla.gnome.org/710691
ok 27 /tls/openssl/connection/async-implicit-handshake
ok 28 /tls/openssl/connection/output-stream-close # SKIP this is not supported with openssl 1.1.1
ok 29 /tls/openssl/connection/garbage-database
# Bug Reference: http://bugzilla.gnome.org/792219
ok 30 /tls/openssl/connection/readwrite-after-connection-destroyed
ok 31 /tls/openssl/connection/sync-op-during-handshake
ok 32 /tls/openssl/connection/socket-timeout
ok 33 /tls/openssl/connection/missing-server-identity
ok 34 /tls/openssl/connection/peer-certificate-notify
# Start of alpn tests
ok 35 /tls/openssl/connection/alpn/match
ok 36 /tls/openssl/connection/alpn/no-match
ok 37 /tls/openssl/connection/alpn/client-only
ok 38 /tls/openssl/connection/alpn/server-only
# End of alpn tests
# End of connection tests
# End of openssl tests
# End of tls tests

Related to #122 (closed) and maybe will close it?