IMO, Mohammad's answer is correct, following an appropriate risk assessment signed off by whatever local authority governs the lab.
If the pseudovirus is replication defective outside of the producer cell line (which it must be, by definition) and has been designed in such a way that recombination to produce an intact SARS-CoV-2 genome is impossible (which it should be) then there's no reason to handle at CL3. Most Institutions would want it to be handled at CL2 however, because it's still an infectious virus (albeit single round) and you don't want your staff exposed to such a thing for all sorts of reasons.
Pseudo viruses do not replicate and they lack virulent genes that's why in my opinion they are not dangerous like real virus but to study them one should must use BSL-2 . As BSL-1 is used for non pathogenic bacterial strains and public access is also not limited in it.