In TLS 1.3, when the client sends its list of supported cipher suites, it guesses which one the server will pick and includes keying material for it in the initial ClientHello. The server does the same in its ServerHello. That reduces a full handshake to 1 round-trip when the guesses are right (vs. 2 RTTs in TLS 1.2).

TLS 1.3 also supports 0-RTT connections for servers the client has connected to before using a static "pre-shared key". There is some additional vulnerability to replay attacks (newly introduced with 0-RTT) and loss of forward secrecy (the same as 1-RTT session resumption in TLS 1.2) of the application data sent in the initial ClientHello. The rest of the data sent in the connection has the full set of TLS security guarantees. The pre-shared key approach has less overhead for servers and a simpler synchronization problem for load-balancers than the session IDs and session cookies of TLS 1.2.

See, e.g., https://blog.cloudflare.com/tls-1-3-overview-and-q-and-a/ for more.

Huge JS ad injectors, JS template renderers and other dynamic stuff adds about 100x more latency on most web pages than anything TLS related.

If you care about client-side latency you should be using HTTP/2. And HTTP/2 is HTTPS-only.

The overhead can be minimized on subsequent connections if you pin a client to one server handling TLS termination for the session (you can either pin to one application server, or a specific load balancer) and your servers have enough memory to keep an adequate number of sessions in memory. You probably take up roughly 10KB of memory per TLS session that's active, so 100 active sessions per 1MB or so which isn't too bad.