Thanks for your feedback everybody. Today I was able to get it somewhat working with LimeSuiteGUI and SDRangel (but not Gqrx) under my Gentoo Linux installation (with much effort). These steps from another thread (including loading the default LDO settings and updating the gateware firmware from 1.22 to 1.24) helped fixing some issues with Linux. At least I now know that the board is not totally broken.
Under macOS I still can’t get it working. This is the output from SoapySDRUtil --probe (running on macOS) as suggested by the previous poster:
######################################################
## Soapy SDR -- the SDR abstraction library
######################################################
Probe device
[INFO] Make connection: 'LimeSDR Mini [USB 3.0] 1D3A0A1D3E0CAE'
libusb: warning [ep_to_pipeRef] no pipeRef found with endpoint address 0x01.
libusb: error [submit_bulk_transfer] endpoint not found on any open interface
libusb: warning [ep_to_pipeRef] no pipeRef found with endpoint address 0x01.
libusb: error [submit_bulk_transfer] endpoint not found on any open interface
libusb: warning [ep_to_pipeRef] no pipeRef found with endpoint address 0x01.
libusb: error [submit_bulk_transfer] endpoint not found on any open interface
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
[INFO] Device name: UNKNOWN
[INFO] Reference: 40 MHz
[INFO] Init LMS7002M(0)
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
libusb: warning [darwin_transfer_status] transfer error: timed out
[INFO] Ver=0, Rev=0, Mask=0
libusb: warning [darwin_transfer_status] transfer error: timed out
Error probing device: ResetChip() failed
libusb: warning [libusb_exit] application left some devices open