In each workspace, right-click on a tab or the tab bar and choose "save all tabs as a speed dial folder". Then, on the start page, edit the folder's name to match the name of the workspace. Then, on the opera://bookmarks page, export your bookmarks. Then, in the new Opera, import your bookmarks and create the workspaces you want. Then, select a workspace, open the start page in it, right-click on the corresponding workspace folder you created and choose "Open all in tabs". Repeat for the other work spaces.
For another way, you could create those speed dial folders and use Opera Sync to sync settings and bookmarks and then open the speed dial folders in each workspace. (Not sure if syncing open tabs honors workspaces yet.)
Another way would be to copy your profile folder (see opera://about for the location) to the new computer before installing Opera on the new computer. Then, lots of things will just carry over. Passwords and extensions won't, but your tabs and workspaces might. Sync can sync passwords too if you want. Or, if you want, you can export them and import them into the new Opera.