Asyncio-based SSL Server not correctly initiating SSL connection

I have an asynchronous server using asyncio and ssl. It works in non-ssl mode but when I switch to ssl it doesn’t connect correctly. I think the error should be in the SSL part because I’ve done a few tests including openssl s_client which returns this:

CONNECTED(00000003)
read:errno=0
---
no peer certificate available
---
No client certificate CA names sent
---
SSL handshake has read 0 bytes and written 194 bytes
---
New, (NONE), Cipher is (NONE)
Secure Renegotiation IS NOT supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
    Protocol  : TLSv1.2
    Cipher    : 0000
    Session-ID: 
    Session-ID-ctx: 
    Master-Key: 
    Start Time: 1672390588
    Timeout   : 7200 (sec)
    Verify return code: 0 (ok)
---

Most of the parts of the output is expected, including no peer cert which I set in both client SSLContext and server SSLContext. The part that worried me was Cipher:0000.
But when I created the context, I used ssl.create_default_context() and changed only no server hostname check (because lack of support of configuring overriding server_hostname in asyncio loop.create_server()) and no cert verify (because I wanted the server to be one-file and not with certs)
Here is my server creation code (with sslcontext definition):

def config_ssl(self):
        context = ssl.create_default_context(ssl.Purpose.CLIENT_AUTH)
        context.verify_mode = ssl.CERT_NONE
        self.sslcontext = context
    def run(self):
        try:
            loop = asyncio.get_event_loop()
        except RuntimeError:
            loop = asyncio.new_event_loop()
        if self.sslcontext is not None:
            coro = loop.create_server(
                lambda: ChatSession(self.addr, self.name, self), 
                    *self.addr, ssl=self.sslcontext
                )
        else:
            coro = loop.create_server(
                lambda: ChatSession(self.addr, self.name, self), 
                    *self.addr
                )
        srv = loop.run_until_complete(coro)
        try:
            loop.run_forever()
        except KeyboardInterrupt:
            pass
        finally:
            srv.close()
            loop.close()

Any help would be apprieciated, and thanks.