Packet sniffer:
Yes, it's that packet sniffer that you linked with the physical device that you linked.
The software can be downloaded on the first page. Unfortunately, it's Windows only
and is not the most stable piece of software. Have not tried it under VMware or
Parallels. However, the software is free and you can try to run it in a virtual Windows
environment.
On iOS, as far as I know, you cannot specify which of the advertising channels to use
as a peripheral. Therefore, you will only succeed with this sniffer with a 33% probability,
as you have to listen on the same frequency as the connection occurs. As there are three
advertising channel and the iPhone most probably is using all of them, the 33% chance
is deduced. In my opinion, it's still a better option for your use case than the other sniffers
that have price tags that are up to three magnitudes higher.