Lost edit after renaming (outside Lightroom)

Your edits are clearly there, as expected. I can't comment about the edit history, because I don't know whether that was there before the photo got renamed or already purged. It's possible that the fact that you relink the image to an image with another name purges it, I never tried. In any case, edit history is not essential. You can change any edits any way you want, because Lightroom edits are non-destructive. You don't really need the history.

"why when I relink missing photo, the file appears to me unedited? In the catalog (still with the old name) I see an edited thumbnail."

If you still have the "old" filename showing in your Catalog, then that is the entitity which you need to "relink".

It has got all your latest edits still in place. Furthermore it has got your prior editing history, Collection membership, any Virtual Copies and all of each one's own edits and metadata too. Stacking, ordering, Publish, print collections, all sorts of evidence of your earlier activity with this photo. Not all of this activity is even possible to write out to XMP, and thus could never get included in a re-import. Since when you do re-import one of these photos you don't see your prior edits at all, AFAICT nothing was previously written out to XMP by LR anyway.

So: you don't want to remove the "old name" image version from LR, because that hold the sole copy of all your prior activity, and this would get deleted if you did so.

You didn't need to do an import: quite the reverse, that is precisely NOT what "relinking" means. This photo IS already imported, and edited, perfectly well: the only problem is that its file-addressing has become invalidated, due to your actions outside of LR. So long as your second import of this photo remains in the Catalog, its mere presence will block you from fixing that first import properly.

So I advise: backup the Catalog for safety, then Remove (without deleting from disk) these second-import image versions. They are of less than zero value to you. Then either:

• if and as you can, rename / move the image files themselves back as they were before - or, bulk restore them from backup perhaps. This will immediately fix everything within LR with no other action needed within the Catalog: to the extent that folders and files on disk, can exactly match their arrangements and namings from before.
• otherwise as necessary, after getting the redundant second-import versions out of the way, re-path each "old name" image file / folder that is still showing. IOW: re-browse each "old name" item so it reconnects onto the respective "new name" item instead (but retains all its history and attributes otherwise).

See LR Help: https://helpx.adobe.com/lightroom-classic/help/locate-missing-photos.html or Locate missing folders 

If you reconnect the images correctly and did not re-import them, then you should not see any differences in Lightroom. The edits should all be there and the edit history too.

First of all, edit history is not saved in XMP, so if you create a new catalog and import raw photos that have an XMP file, then you will get the edits, but not the edit history list.

Secondly, XMP files are only up-to-date with your last edits if you checked the option in the preferences to write changes to XMP, or updated the XMP files manually by choosing the menu to do so. Lightroom does not store the edits in XMP files by default, it stores them in its catalog.