(2022), uses data through to end-2021, when inflation was averaging 4-5%  in the euro area and 6-7% in the US. 9  See Hopkins and Sherman (2021), Byrne et al. (2020), Hodbod et al. (2021) and Datta et al. (2022) for a description of  pandemic consumption trends in Ireland, the euro area and the US.
Overall these institutions do not engage in financial intermediation or credit risk taking, like shadow banks, which do. We could start the list of non-banks in payments with traditional post offices that have been more or less active in payment market for ages. Many have turned into banks or quasi banks by now.