Turned out the issue to be that, maybe I missed, but I did not see anywhere specified that it is mandatory for Infisical be able to reach Kubernetes API.
I thought it could have been the issue and tried to deploy a gateway, but turned out I need to have an Enterprise subscription.(I don't get it, why allow me to go through all steps of configuring a gateway and then in the logs of the gateway return an error for licensing, it should be stated in the web UI IMHO).
Nevertheless I self-hosted Infisical and was able to start testing it.
Thanks for help