... No Client Certificate present in Http Request
This means that the server requires the client to authenticate itself with a certificate. In that mutual authentication not only the server presents a certificate to the client which is then validated by the client, but the client is also required to present its own certificate to the server.
Client certificates are not often used. If they are used it is typically required that you get a certificate from a specific CA or that the certificate you generate some certificate and associate it with your account. The details depend on the actual site and you have to look at their documentation or contact them for details.
I tried making the request with verify=False ...
This only disables validation of the servers certificate and thus has no effect on client certificate related problems.
When I set verify='path/to/request_ca_bundle' I still get the 403 error.
This only sets the trusted CA needed to validate the server certificate and thus has no effect on client certificate related problems.
Note that you get the same error also when accessing the specific URL with your browser. If you don't get this error with the browser you might have necessary certificate installed there. In this case you need to export both certificate and key and then you can use it within the cert
parameter, see Client Side Certificates in the documentation.