Typically such a gateway is intended as part of a LoRaWan (not simply LoRa) network. As such, you don’t actually interact with the gateway but rather with the network server managing the gateway. The RAK7258 does have the option of running a network server task inside box itself, but one installed by a 3rd party is probably pointed instead at their server hosted in the cloud.
So first you need to identify the server in use, then get access to it, then understand the formats it supports.
Traditionally LoRaWan servers only handle “live” data feeds, so they fit publish/subscribe mechanisms such as MQTT. If you want to retain the data in a database and later query it with an API, you need a data platform as 3rd component which supports that.