Before everything was computerised, you'd fill out a form for the PSB when you registered at the hotel, and a copy of that form -- pink I believe -- chopped by the hotel was what you'd use. I'm going to guess that that online form they now use has a "PRINT" button somewhere, but good luck getting the message across to the people at the hotel desk.

EDIT: Do you have Weixin? Apparently the Shenzhen Gong An has a Weixin site on which you can do various things, including registering your residence as a foreigner. This is only necessary if you're not staying in a hotel, since the hotel does the registration for you. Nonetheless, you might browse around the site and see whether there are any options useful to you. There does seem to be a "Query" option.

https://www.wxnmh.com/user-76067.htm (Chinese)
http://bsy.sz.bendibao.com/bsyDetail/618464.html (Chinese)

By the way, be aware of the risk of opening an account in China but not being there afterwards. For example, I just opened up my banking app and got a message that due to new central bank money-laundering rules I have to visit the bank to have my ID documents updated.