In short, the offline installer link at https://www.opera.com/download gives me the 32-bit offline installer instead of the 64-bit (when visiting the page with Chrome Stable 64-bit on Windows 10 64-bit).
And via https://www.opera.com/download, "Download the offline package", I auto-get "Opera_68.0.3618.125_Setup.exe" (32-bit) although my user agent is
from current Opera:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/81.0.4044.138 Safari/537.36 OPR/68.0.3618.125
from current installed MS Edge:
Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/70.0.3538.102 Safari/537.36 Edge/18.18363
and the OS Win64 or x64 version should be detected - and the 64-bit installer "Opera_68.0.3618.125_Setup_x64.exe" should be auto-detected and downloaded.
Someone should change this on Opera website, or isn't it?