Bad Bluetooth signal pick-up

The range will also depend on the antenna used. From the data on that Nano it uses the u-blox NINA module with its own antenna. Knowing u-blox I would have though the antenna would be reasonably good. Is there also a separate antenna pin on the Nano board?

Have a look at the NINA documentation at NINA-B1 series (open CPU) to see how to enable long range mode.