People who legit arrive in HK to claim asylum normally let the Immigration Department know when they arrive (although there a a very few who are genuinely ignorant of how to do things the right way). Non-refoulement claimants go through a fairly tough but by world standards fair assessment of initial claim and, if successful, get handed off to International Social Services for support.
From what I've seen, the vast majority of those begpacking or busking are just trying to fund their travel (or some other) habit. Before Covid, most of them seemed to speak Romanian.
Walk past them and ignore. Or stop and give money. Both are okay.
Moaning about them on the internet though....