Hi Bogdan,
Since curl works, the server must have the correct root certificate.
Under Global Settings → Trusted certificate authorities for SSL, do you have Trust system wide configured CAs turned on?
If yes, then certificate trust is probably not the issue and someone with deeper knowledge of the inner workings of the Slack plugin will need to weigh in.
If no you can either try enabling it or, if there are reasons why it should not be enabled in your environment, you can try downloading the root certificate and manually adding it to Checkmk.
Regards,
Jason