Hello Max,
this won't work, simple rewriting of user's data folder by your backup folder in a freshly installed browser could cause troubles than good.
Better would be to use Avast User's account to synchronize data but I suppose you don't have one.
Now what you can do at least is to rewrite Bookmarks.bak in new browser install with the one from the backup and rename it to just Bookmarks, then you will have your bookmarks back in the browser.
Passwords in this case will be lost.
Sorry for the inconvenience.
I suggest you to create an Avast account to synchronize your data from the browser to the cloud and next time you could just re-install machine/browser and sync your browser's data back.
Hope it will help.
Kind regards,
Josef