How can I recover my Opera browser data after a Windows reinstall?

My Windows installation crashed, and I ended up installing a new version temporarily. All my old files remain on the hard drive, but I didn't back up everything properly, including my Opera browser data. I have several accounts linked to that browser, but I don't have the emails or passwords for them, and losing them would be annoying. Is there a way to manually recover and get my old browser working again from the data on my PC? I'm planning to back up important files and then wipe my system for an upgrade later.