Microsoft Documentation, "Connect to on-premises data sources from Azure Logic Apps": "Before you can connect logic apps to on-premises data sources, download, install, and set up an on-premises data gateway. The gateway works as a bridge that provides quick data transfer and encryption between data sources on premises... After you install the gateway on a local computer, you can then create a gateway resource for the gateway in Azure."
This documentation explicitly outlines the two required components: the on-premises gateway installation and the gateway resource in Azure.
Microsoft Documentation, "What is an on-premises data gateway?": "The on-premises data gateway acts as a bridge to provide quick and secure data transfer between on-premises data... and several Microsoft cloud services. These cloud services include Power BI, Power Apps, Power Automate, Azure Analysis Services, and Azure Logic Apps."
This source confirms that the on-premises data gateway is the correct technology for connecting Logic Apps to on-premises data.
Microsoft Documentation, "On-premises data gateway architecture": "The cloud service stores the credentials for your on-premises data source in Azure Managed Connectors... The on-premises data gateway encrypts and sends the query and credentials to the Azure Service Bus... The Azure Service Bus sends the pending request to the gateway."
This explains the underlying mechanism, which uses an outbound connection to Azure Service Bus, aligning with the scenario where inbound connections are not permitted and Server1 itself lacks internet access (as the gateway can be installed on a different proxy/edge server).