That's not how the TLS handshake works. The TLS server must be configured to request a certificate from the client in order for the client to know that it needs to send a client certificate to the server, and that server-side configuration is disabled for ~99%+ of endpoints.
TLS server implementations should be aborting the TLS connection for violating the TLS Handshake state machine if a client attempts to send a client certificate when it wasn't requested.
So while this bug affects both clients and servers, 100% of clients are parsing the server's TLS cert during the TLS handshake, but less than ~1% of servers are parsing a client's certificate during a handshake.
TLS server implementations should be aborting the TLS connection for violating the TLS Handshake state machine if a client attempts to send a client certificate when it wasn't requested.
So while this bug affects both clients and servers, 100% of clients are parsing the server's TLS cert during the TLS handshake, but less than ~1% of servers are parsing a client's certificate during a handshake.