How to efficiently make REST API call using aiohttp

Question

I trying to write a script which will listen to some TCP message and do REST API to a server using the message. Each REST API call will take approximately 1 second. I want to make it efficient that it process atleast 1K messages per second. I am using asyncio and aiohttp to achieve this concurrently but not getting the expected performance. . I think I am making some fundamental mistake but not able to figure it out.

async def get_rest(session, name, msg) -> None:
    url = "base_url" + msg
    print(f"Consumer {name} before making REST API")
    async with session.get(url, verify_ssl=False) as resp:
        res = await resp.text()
        print(f"Consumer {name} done making REST API")

async def consume(name: int, task_queue: asyncio.Queue) -> None:
    session = aiohttp.ClientSession()
    print(f"Consumer {name} started")
    while True:
        msg = await task_queue.get()
        await get_rest(session, name, msg)

class TCPHandlerClass():
    def __init__(self, task_queue):
        self.task_queue = task_queue

    async def handle_data(self, reader, writer):
        while True:
            data = await reader.read(8192)
            if not data:
                break
            data = data.strip().decode("utf-8")
            lines = data.split("\n")
            for line in lines:
                await self.task_queue.put(line)

    async def asyncio_tcp_syslog_server(self) -> None:
        server = await asyncio.start_server(self.handle_data, '0.0.0.0', 5140)
        addrs = ', '.join(str(sock.getsockname()) for sock in server.sockets)
        async with server:
            await server.serve_forever()

async def main():
    task_queue = asyncio.Queue()
    tcpHandler = TCPHandlerClass(task_queue)
    producers = [asyncio.create_task(tcpHandler.asyncio_tcp_syslog_server())]
    consumers = [asyncio.create_task(consume(n,task_queue)) for n in range(100)]
    await asyncio.gather(*producers)
    await task_queue.join()  # Implicitly awaits consumers, too
    for c in consumers:
        c.cancel()

if __name__ == "__main__":
    asyncio.run(main())

Output:

2022-03-25 05:33:30,660 INFO  [11569] logger: Consumer 43 before making REST API
2022-03-25 05:33:30,660 INFO  [11569] logger: Consumer 44 before making REST API
2022-03-25 05:33:30,661 INFO  [11569] logger: Consumer 45 before making REST API
2022-03-25 05:33:30,661 INFO  [11569] logger: Consumer 46 before making REST API
2022-03-25 05:33:30,661 INFO  [11569] logger: Consumer 47 before making REST API
2022-03-25 05:33:30,661 INFO  [11569] logger: Consumer 48 before making REST API
[>>>>>>>>>>>>>>>>>>>>>100 REST API query done <<<<<<<<<<<<<<<<<<<<<]
2022-03-25 05:33:30,674 INFO  [11569] logger: Consumer 99 before making REST API
2022-03-25 05:33:32,361 INFO  [11569] logger: Consumer 25 done making REST API <<< Started getting response
2022-03-25 05:33:32,361 INFO  [11569] logger: Consumer 25 before making REST API
2022-03-25 05:33:32,368 INFO  [11569] logger: Consumer 20 done making REST API
2022-03-25 05:33:32,368 INFO  [11569] logger: Consumer 20 before making REST API
2022-03-25 05:33:32,369 INFO  [11569] logger: Consumer 15 done making REST API
2022-03-25 05:33:32,369 INFO  [11569] logger: Consumer 15 before making REST API
2022-03-25 05:33:32,423 INFO  [11569] logger: Consumer 10 done making REST API
2022-03-25 05:33:32,423 INFO  [11569] logger: Consumer 10 before making REST API
2022-03-25 05:33:32,424 INFO  [11569] logger: Consumer 22 done making REST API
2022-03-25 05:33:32,435 INFO  [11569] logger: Consumer 4 done making REST API
2022-03-25 05:33:32,703 INFO  [11569] logger: Consumer 56 done making REST API
2022-03-25 05:33:32,723 INFO  [11569] logger: Consumer 11 done making REST API
2022-03-25 05:33:32,750 INFO  [11569] logger: Consumer 7 done making REST API
2022-03-25 05:33:32,794 INFO  [11569] logger: Consumer 16 done making REST API
2022-03-25 05:33:32,801 INFO  [11569] logger: Consumer 0 done making REST API\
2022-03-25 05:33:32,823 INFO  [11569] logger: Consumer 5 done making REST API
2022-03-25 05:33:32,836 INFO  [11569] logger: Consumer 32 done making REST API
[ >>>>>>>>>>>>>>> 100 Messages done <<<<<<<<<<<<<<<<<<<<< ]
2022-03-25 05:33:35,000 INFO  [11569] logger: Consumer 64 done making REST API
2022-03-25 05:33:35,071 INFO  [11569] logger: Consumer 46 done making REST API
2022-03-25 05:33:35,395 INFO  [11569] logger: Consumer 60 done making REST API
2022-03-25 05:33:35,424 INFO  [11569] logger: Consumer 43 done making REST API

I see the all API query is being sent around the same second(05:33:30) and expect the results to be received within ~3 seconds since each REST call will take approx 1 second. But here it take around ~5-7 seconds to complete. How can I make it more efficient ?