The easier way is to Share the published version with your "Team" and then remove the one from your Team. You can replace it with a tab in the Team to the Published version, or you can inside of SharePoint folders (Not in Teams, use Open in SharePoint) where the file was in the Team, replace it with a link to the Published document by clicking "New" Then link. You can link to it, this way when they open the file in Teams where it was previously, it will just link to the Published file, which they now have edit rights too.
If this is a file that needs to be looked over before being published then you'll have to look into two other methods. Either use the above, but turn on the drafts feature on the library the published file is stored. This could have consequences thou if there are a bunch of other files there. This makes it so that everyone see's the "Published" version of the document unless you have full control permissions on the library where you will then see draft's. It's a bit much to get fully into atm but it's something you can use.
The last option would be use a Power Automate flow to copy the file for you. You would have to figure out the trigger on this thou. It could be as easy as setting a metadata flag to trigger, then the flow resets the trigger for next time, or it can be time based etc. Anyway, let me know if you have furthur questions but that's the ones I know off the top of my head.
