
The differences between Windows editions are around functionality, not look and feel. OneDrive and related tools have no bearing on the Windows edition. It is unclear to me what "unified experience" you're looking for and what is different.
If you add your MS account to a local account then you will have access to OneDrive and you can store documents there. However if you didn't set up your machine that way initially then it won't reset it just because you hook up one drive. By default Windows will want to save to OneDrive with your MS account and that is configured at startup. If you didn't associate an MS account then that isn't an option. Open the Settings for OneDrive (open from the tray icon and then go to Settings). From there you can go to Sync and Backup
and configure what you want to backup to OneDrive. You can also control what folders are synced locally.
But what you may consider doing instead is formally switching your local account to your MS account. To do that you need to go into your account settings and there should be a link to sign in with MS account instead of a local account as discussed here. This only appears if you have a local account but it switches your local account over to an MS account. This is different than having your MS account linked to your local account but otherwise won't likely solve your "unified" problems.
Another option is to create a new account on the machine using your MS account. This will create a new profile and you'll need to copy your documents, desktop settings, etc over from your existing local account. Also ensure that you make this new account an admin. Then you can either stop using your local account (but save it for emergency purposes) or remove the account. This is probably the route I'd take unless I already have a lot of app's configured and various personal documents set up as they would all be lost with the new profile.