HTTPS requests in a container don't work

Those are two different layers: of course it is possible to add the ca certificate used by TLS inspection to the docker demon. As TLs inspection breaks the security context to the registry, you will need to treat it like a secure private registry:

Note: myregistry:5000 is just an example fqdn for a private registry.

The ca.crt used by the tls inspection must be placed in /etc/docker/certs.d/{fqdn of the registry}/ca.crt
I don’t recall whether the docker demon needs to be restarted to actually use the certificate.

On Docker Desktop for Mac the solution can be found in the faqs:

I assume you mean the image, as it would be tedious to inject the certificates manually into each container.

Update: fixed a wrong wording