HTTP Connect

HTTP Connect is message the is sent by Web Client to forward proxy. It is never sent by web Client to Web server
That means when in (Browser Settings > Proxy > Proxy Server) is defined then only browser generates the HTTP Connect message.

Web-Browser                                                   Forward-Proxy
          HTTP CONNECT www.example.com:443 HTTP/1.1
          Host: www.example.com:443
          Proxy-Connection: Keep-Alive
          User-Agent: Mozilla/5.0 ...
          Proxy-Authorization: Basic dXNlcm5hbWU6cGFzc3dvcmQ=
          ----------------------------------------------------->

                            HTTP/1.1 200 Connection Established
                            Proxy-Agent: Squid/5.7
          <-----------------------------------------------------
      

Why HTTP Connect is Required?

To understand why the HTTP CONNECT method is used, we need to talk about forward proxies (web proxies)
Web Client sends request to intermediary proxy server to request permission to pass through.
When you connect to an HTTPS website (which uses TLS encryption), your traffic is encrypted. If you are behind a corporate firewall or using a web proxy, that proxy needs to route your traffic. However, because TLS is encrypted end-to-end, the proxy cannot read the application data (like the specific URL path or headers) to know where to send it.
More importantly, if the proxy tried to intercept and read the TLS handshake directly, it would break the security chain (resulting in a certificate warning). To solve this, the client uses HTTP CONNECT to tell the proxy: "Please just open a raw TCP pipeline to this specific domain and port, and then step out of the way." Once the proxy establishes that connection, it blindly forwards data back and forth, allowing the client and the destination server to perform their private TLS handshake directly through the proxy.

Sequential Order of Traffic

1. TCP Handshake: Client --> Proxy (SYN, SYN-ACK, ACK)
2. Proxy Tunneling: Client sends HTTP CONNECT to the Proxy.
3. Proxy Approval: Proxy connects to the destination server, then sends 200 Connection Established back to the Client.
4. TLS Handshake (End-to-End): Client sends TLS Client Hello through the proxy to the Destination Server.
5. Encrypted Data: Standard encrypted HTTPS traffic flows through the tunnel.

Direct Connection (No Proxy = No HTTP Connect)

When you are at home on your personal Wi-Fi, your browser typically has a direct route to the destination web server. In this case, your client doesn't need to ask an intermediary for permission or routing help. It just initiates a TCP handshake directly with the web server's IP address and immediately sends the TLS Client Hello. HTTP CONNECT is completely absent from this workflow.
OR that means Proxy is not configured in User's Browser Settings.