"Which servers / sites support HTTP/1.1. pipelining?"

There are probably millions. IME, over 20 years of using pipelining, it is quite rare to find ones that don't. Here is a simple example.

Download the k-tree transcript archive from stackexchange.com

1116 HTTP requests, 1 TCP connection

26MB download

        stunnel -fd 0 << eof
        debug=debug 
        pid=$HOME/1.pid
        foreground=no
        [ x ]
        accept=127.0.0.77:80
        client=yes
        connect=198.252.206.29:443
        options=NO_TICKET
        options=NO_RENEGOTIATION
        renegotiation=no
        sni=
        sslVersion=TLSv1.3
        eof 
        export Connection=keep-alive; 
        sh -c "$(sh -c "$(seq -f "seq -f 'seq -f "https://chat.stackexchange.com/transcript/90748/%g/%%g/%%%%g" 1 31' 1 12" 2019 2021)")" \
        |a.out \
        |nc -vvn 127.77 80 > 1.htm
        cd;kill $(cat 1.pid)

        cat > 1.l         

        int yy_get_next_buffer();
        int fileno(FILE *);
        int setenv (const char *, const char *, int);
        int dprintf(int, const char *__restrict, ...);
        #define httpMethod "GET"
        #define httpVersion "1.1"
        #define Host ""
        #define jmp BEGIN
        #define Y(x,y) fprintf(stdout,x,y)
        int count,path,ka;
        int httpheaders(){
          setenv("httpMethod",httpMethod,0);Y("%s ",getenv("httpMethod"));
          Y("%s HTTP/",getenv("Path"));
          setenv("httpVersion",httpVersion,0);Y("%s\r\n",getenv("httpVersion"));
          if(0==setenv("Host","",0))Y("Host: %s\r\n",getenv("Host"));
          if(getenv("Connection"))Y("Connection: %s\r\n",getenv("Connection"));
          fputs("\r\n",stdout);
          return 0;}
    %option nounput noinput
    %s xa xb xc
    xa "http://"|"https://"
    xb [-A-Za-z0-9.:]*
    xc [^#'|<> \r\n]*
    %%
    ^{xa} count++;setenv("Scheme",yytext,0);jmp xa;
    <xa>{xb} setenv("Host",yytext,1);if(!getenv("Host"))setenv("Host",Host,0);jmp xb;
    <xb>\n path=0;setenv("Path","/",0);httpheaders();jmp 0;
    <xb>{xc} path=1;setenv("Path",yytext,1);httpheaders();jmp 0;
    .|\n
    %% 
       int main(){yylex();exit(0);}
       int yywrap(){if(count>1){
         fputs("GET /robots.txt HTTP/1.1\r\n",stdout); 
         Y("Host: %s\r\n",getenv("Host")); 
         fputs("Connection: close\r\n",stdout);
         fputs("\r\n",stdout);};
         exit(0);}

      ^D

     flex 1.l
     cc -std=c89 -Wall -pedantic -static -pipe lex.yy.c