You can test TLS version on a website with either OpenSSL or Nmap.

Nmap includes a script to check SSL/TLS versions. The grepped version just shows the TLS versions supported. More info on the Nmap script on nmap.org.

nmap -sV --script ssl-enum-ciphers -p 443 example.com

nmap -sV --script ssl-enum-ciphers -p 443 example.com | grep TLSv

To test with OpenSSL you have specify the version. The -servername option is needed if the server uses SNI to host multiple sites.

openssl s_client -connect example.com:443 -tls1   -servername example.com
openssl s_client -connect example.com:443 -tls1_1 -servername example.com
openssl s_client -connect example.com:443 -tls1_2 -servername example.com

If the site doesn't support that TLS version you'll get something like this. If it works you'll see the cert in hex and a bunch of other stuff and it will leave the connection open so you'll have to hit ctrl-c to disconnect.

CONNECTED(0000020C)
37556:error:1409442E:SSL routines:ssl3_read_bytes:tlsv1 alert protocol version:ssl/record/rec_layer_s3.c:1544:SSL alert number 70
---
no peer certificate available
---
No client certificate CA names sent
---
SSL handshake has read 7 bytes and written 120 bytes
Verification: OK
---
New, (NONE), Cipher is (NONE)
Secure Renegotiation IS NOT supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
    Protocol  : TLSv1
    Cipher    : 0000
    Session-ID:
    Session-ID-ctx:
    Master-Key:
    PSK identity: None
    PSK identity hint: None
    SRP username: None
    Start Time: 1709754202
    Timeout   : 7200 (sec)
    Verify return code: 0 (ok)
    Extended master secret: no
---