If you put “performance materiality” into the search feature you will find various similar posts – for example this one https://opentuition.com/topic/performance-materiality-11 explains why performance materiality is lower than overall materiality.
Lower materiality corresponds to large sample sizes is just “commonsense”. Think about what it means in terms of $s. For example, if performance materiality if $100k and I tell you to examine all items in a population > $100k you might tell me that you have examined 12 items. If I then say – sorry – I meant $10,000 – will you be examining more or less than 12 items?