Goldman Sachs initiate STX at Buy, page-18

The register will be right up to date. It will reflect each trade when settled - so about 2-3 days behind (maybe better than that these days?)
When you request a viewing, often you have to sign a waiver, stating variously that you won't use info for commercial use etc.
Usually the Registry will get the permission of the company to allow you to view the register --- BUT that Register is a public document - and you do not need to be a shareholder to view it. But easier to get permission if you are.
Sometimes you can view a hard copy of register, sometimes (usually these days), it is online. Sometimes they make it difficult, and you need to insert a name to view details - and others you just scroll thru.
I don't think a shareholder will get any grief from STX if they wanted to go to the trouble of viewing the register.
Take a pen and paper!

I think Boardroom has offices in Sydney, Melb and Brisbane, so you can request to view it at one of those offices. Good luck.
(I am not in that Top20 - more's the pity)