For the manual, non-Sync way (that you should do regardless as a backup, even if you upgrade Windows 10 to 11 instead of installing 11 fresh):
For passwords, goto the URL opera://password-manager/settings and export your passwords to a CSV file. Then, open that CSV file in a text editor to make sure they're there. Then, copy the csv file to a USB stick. Then, in the new Opera on Windows 11, goto the URL opera://password-manager/settings again and import that CSV file.
For bookmarks, goto the URL opera://bookmarks and use the drop-down at the bottom left to export your bookmarks to an HTML file. Then, copy the HTML file to a USB stick. Then, in the new Opera on Windows 11, goto the URL opera://settings/importData, select "Bookmarks HTML file" in the drop-down and point it to the HTML file to import it. Then, goto the URL opera://bookmarks and go into the "Bookmarks Bar" folder to see your imported bookmarks. You can them move the imported bookmarks to where you want like the "Other Bookmarks" folder or the "Speed Dial" folder or the root of the "Bookmarks Bar" folder. This method will not retain customized thumbnails for your speed dial icons though.
Note that the opera://bookmarks page works a lot like Windows Explorer (File Explorer) where you can select or select all (ctrl + a), copy (ctrl + c), cut (ctrl + x) and paste (ctrl + v). You can also copy/move with the mouse. You can move by dragging for example.
For open tabs, before you export your bookmarks, you can right-click on a tab, goto "Save" and choose "All tabs to a speed dial folder". Then, in the new Opera, after you import your bookmarks, you can right-click on that speed dial folder and choose "open all in tabs" to get your open tabs back. If you use workspaces in Opera, you can save all tabs to a speed dial folder in each additional workspace you have. Then, in the new Opera, after importing the bookmarks file and manually creating your extra workspaces again, you can switch to each one, right-click on its corresponding speed dial folder and chooes "open all in tabs". This method will allow you to get all tabs in all workspaces back.
For history, you can goto the URL opera://about, take note of the "profile" path, close Opera and copy the "History" file in the profile folder to a USB stick. Then, in Windows 11 with the new Opera, goto the URL opera://about, take note of the "profile" folder, close Opera and replace its "History" file with the one from your USB stick.
Note that in Windows Explorer (File Explorer), to be able to see your "C:\Users\yourusername\AppData" folder to get to Opera's profile folder, you'll want to click "View" on the Explorer toolbar, goto "Show" and enable "hidden items". You should also enable file extensions. Do those things in both Windows 10 and Windows 11.
As for extensions, you'll need to reinstall them.
As for logged-in sessions, you'll need to sign into sites again. But, that should be quick if you do it after importing your passwords.
As for settings, you just have to reconfigure them.
