From what I have read, Red Army officials were quite sceptic about handheld AT weapons supplied from the US and UK. They were quite happy with their PTRD and PTRS rifles and wanted something with similar range. That seems to be the reason why the Bazooka did not see much use and it might also be the reason why the PIAT wasn't used at all.
http://tankarchives.blogspot.com/2017/08/lend-lease-impressions-bazooka.html
Sadly, I can't read the original source they linked.