Question about restore/migrate (non urgent)

My question concerns the URLs in the WordPress database:

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Super Quick Migration automatically changes URLs?
I created a backup on one of my online sites and moved it with the Super Quick Migration to an installation on “Local for WP” on my computer.

That worked like a charme and felt like magic. Thanx for that.

As everything worked and I don’t remember searching and replacing URLs I assumed that that had happened automatically. Is that so?

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Restore does not change URLs?

I now have updated the site on Local and wanted it to get it back to the online webspace. Using the Super Quick Migration doesn’t work as a domain like website.local can’t be resolved.

So I uploaded the backup and used “Restore”. Now the URLs were not changed automatically and images didn’t show up.

That’s easily fixed with a plugin like Better Search and Replace, but I wondered if there is a better way from the Local installation back to the online-webspace. A kind of Super Migration without the URL.