@David Macháček Thanks for getting back, this will not work from portal test console as i see from the screenshot that you're making a call to http://sgc-apim-prem.azure-api.net/request the host name gc-apim-prem.azure-api.net will resolve to Ip address of your APIM instance. Can you please try with postman as below with AKS ip address.
By this way you can verify that the self-hosted gateway is configured correctly, and that the API is accessible through the SHG.
do let me know incase of further queries, I would be happy to assist you.