> it's "just" slow start making it slower
Six connections with H1 means waiting for the server to process only up to six responses at a time. You also can't send any additional requests until one of those six ongoing requests has finished. So at the very least, you're paying a full round trip cost per request where no useful work is happening.
Let's say the server makes a 250ms request to an auth service on each request. For every six requests, you're sitting and waiting a quarter second for the server to sit and wait. With H2, you essentially pay that 250ms cost once, because ~every request happens concurrently. With H1, you pay it once per request on each connection.
It's also the case that many servers stream their responses. If I make 12 requests and the storage that the server pulls the data from responds more slowly than the server can send it to the client, H2 means that I get twelve half finished requests instead of six half finished requests and six requests that never even got sent. For content that doesn't require the full file to be loaded, that's a win.
H2 also has header compression. Sending HTTP requests on H1 often takes multiple packets, especially if you have more than one cookie. HPACK can basically eliminate much of the overhead of actually sending the request, eliminating multiple TCP round trips. Which means the server is able to start processing more requests in parallel sooner because it's not waiting for the requests to arrive as long.
H3 eliminates many of the problems caused by head of line blocking. If you have packet loss on one of your connections, whatever was being transmitted is now blocked until TCP sorts out the missing packet. H3 limits the congestion only to the individual request impacted by the lost packet rather than all of the requests being made over that connection.
In any case, it's not "just" TCP slow start that makes H2/H3 better than H1 in regards to concurrency.