Coroutinize http client code

include/seastar/http/client.hh

@@ -128,8 +128,6 @@ public:
 private:
     future<reply_ptr> do_make_request(request& rq);
     void setup_request(request& rq);
-    future<> send_request_head(const request& rq);
-    future<reply_ptr> maybe_wait_for_continue(const request& req);
     future<> write_body(const request& rq);
     future<reply_ptr> recv_reply();
 
@@ -193,11 +191,11 @@ private:
     future<> shrink_connections();
 
     template <std::invocable<connection&> Fn>
-    auto with_connection(Fn&& fn, abort_source*);
+    futurize_t<std::invoke_result_t<Fn, connection&>> with_connection(Fn fn, abort_source*);
 
     template <typename Fn>
     requires std::invocable<Fn, connection&>
-    auto with_new_connection(Fn&& fn, abort_source*);
+    futurize_t<std::invoke_result_t<Fn, connection&>> with_new_connection(Fn fn, abort_source*);
 
     future<> do_make_request(request req, reply_handler handle, abort_source*, std::optional<reply::status_type> expected);
     future<> do_make_request(connection& con, request& req, reply_handler& handle, abort_source*, std::optional<reply::status_type> expected);