Background task with MFi External Accesory device

We are developing an app that is going to be used with hardware that is connected through bluethooth to the iOS device, where we use a device with an MFI external accessory, and we are using the external accessory framework, and this will require some background tasks, we understand that there is a limitation on the use on background capabilities, but we were wondering what is the best approach to gather information from the hardware while the app is running on the background? think of the Oura ring, the app is gathering some information while you are sleeping, not processing, not fully running, only gathering information. Should we doit with the BGProcesingTask? or there is an additional background strategy to this kind of use case?

Thanks.