Kendra Little links to a Connect item:
Can you change the filegroup where Query Store keeps its data?
I thought there might be a trick to use a different filegroup for Query Store by using the default filegroup setting in SQL Server before enabling it, but NOPE!
I concur; Query Store can grow to be pretty large on busy systems, so diligent DBAs who want to keep PRIMARY as small as possible will suddenly find a multi-gigabyte Query Store slowing down those PRIMARY filegroup restores.